What is the max amount of lift a stock GM 088 head can handle?

I take a stab at it - as far as I know, the HP500 engines were running basically stock 088 heads, with the exception of 2.25 intake valves and inconel exhaust valves, along with better springs than the heads come with from GM. I think the HP500 cam is a little under .600 lift at the valve, so you should be OK with something in that neighborhood. That being said, it is up to the engine builder to carefully check things like coil bind, retainer to guide clearance, valve to piston clearance, and proper valvetrain geometry when installing a cam. You will also have to properly set the valve installed height to get the proper spring pressures for the cam profile you are running.

All of this stuff has to work together. When you mix and match parts like springs, retainers, etc., you can get yourself into trouble. What kind of cam are you planning to install?