The hydrualic lifters could fail if the oil pump is:
1. Worn and not producing ample oil pressure, 10 to 20 psi usually.
2. The pressure regulator valve is stuck,jammed or worn as well.

Changing oil from petro to synthetic was a lost step. Oil is oil for cars and the only benifit of synthetic is that it lasts longer.
Although it appeared to help, it is not the solution.

Check for timing belt condition, skipping a tooth will cause low compression and poor performance. Perform a leak-down on each cylinder to asertain if the valves are closed at TDC.
Finaly, see if the exhaust is blocked by a distroyed cat converter.