well i would first check the oil. if it is ok, ie no coolant, good level, etc. Then i would check compression.

If it will run, and the compression is good, then you could do couple things to check/fix the lifter tick. But make sure the rest of the engine isn't bad.

MY question is kind of answered, because it runs correct? that how you know there is lifter noise? So fix the thermostat housing. And give it an oil change. If the tick gets worse or better in the next 50 miles. we can go from there. But verify oil pressure, and oil to the head.