did you use a hydrolic of solid cam.
hydrolic cam shouldnt have a tick. and they should hold a rather constant pressure
now i dotn mean to offend you in any way but, did you think it could be the oil setteling out of the head. when the motor sits the oil drains down, when this happens the motor on start up has to pump the whole motor full again. it has to get it all out of the pan into the whoel motor. if its only a few seconds i wouldnt worry about it to much, motors make weird noises.
the amc 360 has a oiling problem to begin with. the oil passages and all arent big enough in soe spots and the pan istn dep enough for therse motors. the rear 2 main journals dont get enough oil therefore dont last as long as say a 350 chevy.
you can do 2 things to solve this. there is a stainless line you can put in the valley of the motor, under the intake manifold. this will send the oil from the front oil passage to the rear getting the oil there faster.
second, milidon sells a swinging doule pick up setup for the amc motors that will pretty much eliminate this problem. pumps oil everywhere and picks it up in 2 spots. kinda pricy though.
for the lifters check the clearences and if it presists and the motor still runs fine, id let it be.