Kohler cv15t won't start

This unit was getting harder and harder to start. Today it won't start. New plug and gas filter.... it won't fire with starting fluid . It did backfire in carburetor once. I didn't have spark tester but pretty sure getting spark. Now I am thinking hydraulic lifter problem due to backfire? What is the practical way to test those? This is a very old engine.

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View attachment 328338