My Lady Kenmore dryer runs but won't heat. What is the problem?

Its broke.

Could be a burned out heating element, thermostat or other fault... nobody can say for sure without someone that understands these things and has the equipment looking at it.

Most likely it is dirty and lint deposits have built up, as it always does, in all the air ducts which will cause the main safety to blow or element to burn out from being overworked or just from age. You need a multi-meter to find which safety has blown or if element is bad as well as fuses on each end of element. You will have to take it all apart. You will have to clean the drier out thoroughly or it is all for nothing. Every air duct will have to be removed and scraped and washed out to remove baked on lint deposits which bakes on like a concrete lining. This will burn so the manufacturer has installed the safeties to keep from having a house fire. The safeties are oval-shaped with a round center part containing the safety with two plug-on terminals for the wires and when they burn open, from the dryer being dirty, nothing will work. Using an ohm meter you put a lead on each terminal of the safety, with one wire unplugged, and if it is good you will have a reading of about zero; if it is bad it will read infinity. Driers were the number one cause of fires at one time, hence now we have safety fuses. Look at: How to clean your clothes dryer. How to make it hot again. - YouTube (http://www.youtube.com/watch?v=MMP7BW1lLs4) to see how. Also look at these to get an idea about how to clean it: Mr. Appliance Tips: How to Clean Your Dryer - YouTube (http://www.youtube.com/watch?v=iBiRw-KElC4) ; Cleaning a Dryer Vent and Lint Trap - YouTube (http://www.youtube.com/watch?v=yFTZGgVisCI)
Electric Clothes Dryers (http://www.electrical-forensics.com/Dryer/ElectricClothesDryers.html) Dryer vent cleaning prevents fires - YouTube (http://www.youtube.com/watch?v=A6wmD502-xE) and: Cleaning out a dryer with top lint cleanout - YouTube (http://www.youtube.com/watch?v=OBNDbyRm68M&feature=fvsr)
Cleaning out a dryer: By a woman 2 of 2 - YouTube (http://www.youtube.com/watch?v=a73HTFkcB90&feature=relmfu)
Whirlpool Dryer Model LE5800XSW3 Wiring Diagram | Dryer Repair | Fixitnow.com Samurai Appliance Repair Man (http://fixitnow.com/wp/2010/10/09/whirlpool-dryer-model-le5800xsw3-wiring-diagram/)
When you finish cleaning the drier it is best to also replace the belt, too, because you do not want to have to disassemble it all over again and if the belt is over two years old you should replace it.

Note that on most of the videos it does not show them washing out the parts, but this is important because it's the only way to really get the parts clean, just don't get motor wet or the capacitor if it has one. Vacuum out the motor to remove all dust. I would move the drier out to your garage to have plenty of space to work. You also want to check your vent and clean it, also. The vent should have a short run and be straight as possible. The job is really easier than it sounds. There is no shortcut that will work; it has to be cleaned well. Before you re-assemble it make sure to use white lithium grease (high-temp grease) and grease all bearings. Just vacuuming out the dryer a little does little good. DrTom4444