Knackered Impluse coupling on left Mag? Mag P leads crossed over?(this is the usual suspect) Blocked Primer Nozzles? Carb accelerator pump diaphragm ruptured. Knackered camshaft or cam followers upsetting the valve timing (quite possible on a high time engine) Spark plug gaps incorrect? Have you had the prop off lately and it's been refitted out of phase? (Shouldn't be possible with the master dowel on the flange but you never know). Starter ring gear and flywheel incorrectly fitted making a nonsense of the timing?
Three or squirts with the primer followed by a couple of pumps with the throttle should start any Lycoming from cold without risk of flooding.