Installing LED under counter lighting with dimmer switches - 1 switch for left of sink; one for right. Replacing previous switches that controlled all lights with R switch and disposal with L switch. Separated light wiring from R switch; removed disposal wiring completely. Have single hot, common and ground to J-box. Connected both dimmer hot (black) to hot (black), both dimmer ground (green) to copper ground. All common (white) connected together. Connected each hot from dimmer (red) to the hot to lights (separate wiring, obviously not connected together). Verified this arrangement. When power restored, current runs to L lights, but only runs to R lights when L switch is on as well. (I.e L switch off, no power to R at any time.) Am I missing something obvious? Tried 2 different dimmers on R - same result. Dimmers are the recommended Lutron for these LED fixtures. Tested dimmer on L lights and works perfectly. What could be up with the R?

I don't think I follow all of what you said. Particularly

Connected both dimmer hot (black) to hot (black),

You don't say where the power is coming in to. I suspect that it is coming into the box under the sink and that the power originally went from there to the switch on th right. The wiring between the box an the switch on the left would have been a switch loop for the disposal. Suspect that now the power comes into the box under the sink, goes to the switch on the left and back to the box. From there it goes to the switch on the right.

Therefore there will only be power at the switch on the right when the switch on the left is on.

Or, maybe I'm just confused. What's the wiring in the box?

I think you need to swap 2 wires, verify incoming.
Verify Hot first, try without dimmer, then add dimmers, swap if necessary to determine which parts may be defective.
I take it this doesn't use a relay box?

Wiring in box from panel is black (hot) white (common) and ground (green). Originally, the double box contained 2 switches; the left turned on an outlet under the sink, giving power to a disposal. The right switch controlled all under cabinet lighting (to the left and right of the sink). I disconnected the outlet wiring from L switch completely. I removed the wiring for the lights from the R switch, separating the wiring for L and R sides. Now, I'm wiring just the L side lights to the L switch and R to R. Using the single hot wiring (assuming from the panel), both black dimmer wires are joined with the black hot; both green grounds are joined to the bare copper; the red hot out of the dimmers are separately connected to the black to the corresponding lights. All white commons are joined together. The L side is working - I've connected lighting to the wiring and operated the dimmer for that side with no issues. The R side shows no power to the lights until the L switch is turned on. L switch off, no power to R lights. I'm not an electrician at all, but it seems all wiring I did is correct. Could there be something behind the walls that would cause this? The R switch originally controlled all the lights; all I've really changed is the removal of the L side lights.
Also, have tried 2 different, new dimmers on the R. Same result.

I'm really confused! Thanks for your help!

I think I'm beginning to understand but not sure about some things.

You had a two gang switch box above the counter top with two switches in it. You had a receptacle in the cabinet under the sink that you plugged the disposal into. One of the switches turn the disposal on. The other switch turned on some under cabinets light. How many cables were in the switch box when you started? I'm guessing that there was two cables, each with a black and white wire, plus the wires for the under cabinet lights.

I'm also guessing that the under cabinet wires were not the regular Romex cables used for house wiring.

You say you removed the switches and separated the under cabinet wiring. You said you remove the disposal. What does that mean? Does that mean you unplugged the disposal or does it mean you change the wiring to the disposal.

Tell us exactly what you did from the beginning before you attempted to install the dimmer switches. Are the under cabinet lights sets of light fixtures or are they individual lights that you wires up.

In the original box there were 4 "sets" of cable (Romex), each with black, white and copper. Each switch was connected to the "power" cable (from the panel), cable #1. The left switch then carried power to the outlet box (for disposal) on cable #2, and the lights were connected to the right switch via #3 and #4. I disconnected #2 from the L switch, effectively eliminating the outlet box. #2 is no longer connected or in use anywhere. #3 (L side lights) was connected to the L dimmer switch as previously described; #4 to the R switch. Lights are LED bars that connect direct to 110v house current - first bar would connect to power; additional bars can be linked by cable. Other than the test done on the L side, no bars have been installed.

The original switches were simple single pole toggles. All I was attempting to do was to re-route the control of the outlet to control the L bank of lights, leaving control of the R bank on the R switch. Probably my biggest mistake was thinking this would be an easy process. Duh!

If you have to have 1 switch on for the other to work.
Determine EXACTLY which wire is hot, that goes to the 2 dimmers/switches, then out to each set of lights.
Swap lights to test if needed. You have 2 of everything and allows the ability to determine a bad part, by swapping.
Make them work with switches, then install dimmers.

It is easy, just you made some simple error somewhere. We all do it. That's why I am trying to be so specific.

What did you do with cable #2, the one to the disposal? Did you remove it or just leave it unconnected in the switch box.

Cable #2 (previously connected to the outlet) was disconnected from the L switch. There is no power in that cable, so I taped it off (overly cautious?) and left it behind the J-box in the wall space.

Now I'll admit I never checked to verify on the power source if BLACK was hot and WHITE was common, but if it were reversed, nothing would be working at all, right?

By the way, you guys are up way too late and way too early to answer questions like this! :-)

you guys are up way too late and way too early to answer questions like this! :-)
No rest for the wicked.

Here is what I suspect is going on.

Power is being fed to the outlet in the cabinet. From there there are two cables going to the switch box. One was uninterrupted power to the original light switch. The other was a switch loop for the disposal.

When wiring a switch loop, power is taken from the fixture box (in this case the outlet box) to the switch box on the white. Power is returned to the fixture (outlet) on the black.

I also suspect that the under counter light were installed after the original wiring was done. Otherwise the installer would have most likely taken the power to the switch location and then to the disposal. It is not at all unusual to split the outlet for a disposal outlet like this. Making one half of it switched and the other half of it hot all the time.

I suspect that you have incorrectly identified which cable is the uninterrupt power and which is the disposal switch loop. That would explain why the second switch will only work when the first is on. Power to the under counter light is coming in on the white and going to the lights on the white wires. It is then returning from the lights to the switch on the black. In effect you are interrupting the neutral of the light circuit. The second light is getting power after the switch.

Another possibility is that in capping off the switch loop you mistakenly capped the white of one cable and the black of another.

However, there is something else going on and I'm not sure what it is. For what I have described as possible errors, you should either trip the breaker or nothing should work. I suspect that the "something else" is in the outlet box wiring.

Suggest that you pull the outlet and examine the wiring there. Are you familiar with switch loop wiring and split outlets?

The error may very well not be yours. May be in the wiring in the outlet. Check for the possible errors. Tell us how you identified the uninterrupted power cable from the switch loop. Pull the outlet and describe the wiring.