I found this website by trying to find out what was causing the oil pressure light on my 2003 LK3054 to come on. I saw that you were having similar problems. I am not a mechanic but I do like to get to the root cause of the problem.
The first thing I did was to find out what the normal operating oil pressure is. In my case it is between 35-60psi.
Next I replaced the oil sending unit. It didn't help.
Then I ordered a $9 oil pressure gauge from Harborfreight and hooked it and the light up. The gauge confirmed that the light was working properly. The light is supposed to go off at 7psi. It did!
When I first start the tractor I had about 30psi and within 5min. I was down to 10psi. When the tractor was completely warmed up and working the light would come on and the gauge would read 5-7psi.
I was told to check the oil pressure relief valve to make sure that the spring was not broken or weak. I did that. It appears to be OK.
By the way, on my tractor it is located behind the oil filter so you have to take the filter off and undo the nut that holds the filter in place to get to it.
The thing I didn't know was that diesel engines use different oil formulation then gas engines. The oil for deisel engines has an API desination that starts with a C. The latest API designation is CI-4 to the best of my knowldege. The last time I changed oil I put in oil designed for gas engines. This has an API designation that starts with an S.
I am changing oil in the morning to see if that solves the problem. If not, It is most likely a bad oil pump.
Hope this helps.