I bought a car recently with block casting number 14093638. From other forums, it is suggested that it has a roller cam in it. I plant to verify that by checking my push rod length. It has aluminim heads on it with roller rockers. They are Competition Cams aftermarket rockers, so it would be a fair assumption that it has an aftermarket cam in it. Here's the kicker, no cam card came with the car and the guy I bought it from didn't have a clue, so I am blind on what it is. Without tearing it appart down to the cam and checking the P/N, how can I figure what the lash should be set at? Any suggestions?  

You're pretty much screwed on this one. The nose of the cam will have a part no. on it, but you'll have to remove the front of the motor and timing cover along with chain to figure that out.

The only other option is to get a dial indicator and measure the lift at the valve on both intake and exhaust, and go through the Comp catalog looking for a cam with the same lift. Problem is, this method leaves a ton of room for error.  

Nice.  

Just because it has roller rockers, dont assume it has a roller cam. Like you said, a look at the pushrod lenght will tell you. But only if it's a hydraulic cam. If it's a solid roller the pushrods will be the same lenght as a flat tappet cam, hydraulic or solid. There is zero lash on a hydraulic cam. Like 55guy said, you can mount the dial indicator and degree wheel to find all the specs on that cam.