My water pump (3/4 HP), which is at least 5-10 year old has lost the ability to retain pressure. I thought it might be the pressure tank, however, I turned off the feed from the pump to the pressure tank and it still lost pressure. This makes me believe that the pump is the problem. I draw water approx. 20ft to the head, from a fresh water lake. I would appreciate any assistance as a replacement pump is approx $400. Can the pump be repaired (i.e. seals replaced). I am guessing the pump will last a few more days before it ends up burning out as it cycles every 1-2 minutes to keep pressure.

Is there a chance it is a vaulty check valve, and if so how can you open the pump and replace it? I am a backyard mechanic that know little and is willing to learn. I read in a similar post, that a check valve and foot valve are the same thing. Considering the foot valve is probably 20 ft down in the lake, is there a way I can test this, or are my symptoms of losing pressure (with the pressure tank shut off - house cut off from pump) a easy sign of a replacement?

Consider I am pulling from a lake is there a chance some sand/silt has gotten between a seal somewhere, and finally, are these pumps worth fixing (are they serviceable)?

I really appreciate the help from the experts.

I think you have two problems.
First is a faulty check valve that allows pressurized water to backflow toward the pump. It's probably not in the pump assembly itself but certainly upstream from the point where your first point of water use is i.e.. where the house draws water from the system. These valves come in different configurations but you see it as possibly looking like a largish shutoff valve with no handle.
Second, you may have a pressure tank that is full of water. If so, there is little or no air in the tank for the pump to compress so any, and I mean any, loss of water in the house from a leak will cause your pump to cycle often. There should be an air valve on the tank for the express purpose of replacing this air "pocket". Over time, this air is absorbed into the water system allowing the water level to rise in the tank. Pump some air into the tank and pump cycling problem is solved.
You'll still want to repair any leaks. Then if there is a valve that you can turn off that will isolate the house but retain pressure on the check valve, and the pressure still drops, you need a new valve.

Good answers and should be looked at but also if you are pulling water from a lake a good chance the foot valve(check valve) is dirty or clogged with grass or other matter. Pull it off, clean it and try again. Let us know. Good luck.