Can discharge from the penis be found in a urine lab test?

Sometimes. Depending on when/how much exited with the urination and if getting a "dipstick" test or spun / formal urinalysis (which is more likely to identify it). Absence does not clear you of having an std, but yes, can sometimes id from urinalysis.
Discharge is STD. Not unless the urine test was specifically requested to test for gonorrhea and chlamydia.