I think that my mechanical fuel pumped is gone on my carbed 86 lg4. Are there any tests that i can perform to check the pump?

 

You could disconnect the line from the carb, and see if lots of fuel comes out when you crank the motor. If it doesn't, just change it out. It's like 15 minutes and $12. I sent my wife down the street (about ¾ mile) once to get a new one; while she was gone I discovered I had one in stock; by the time she got back, the car was already running. Not worth the trouble of futzing around much more than that if it costs even as little as an extra 5 minutes.

If the pump works, change the fuel filter; and if the pump doesn't work, change the fuel filter. So I guess I'm saying, if you think you have fuel delivery issues, change the fuel filter. It's inside the carb fuel inlet nut, where the line screws into the carb.

 

Try squirting a little starting fluid into the carb.If it fires, it could very well be the fuel pump, but definitly change the fuel filter first if you haven't done that in a while.
It's a whole lot easier, and cheaper, ir it's not the pump.