2005,Will it damage my Honda Civic Hybrid 2005 engine to drive it with a bad lifter? 2005 Honda Civic Hybrid

The car runs fine and gets about 40 mpg with no A/C running. It taps on cold acceleration, but the tapping usually goes away when it warms up. The engine is a rebuilt replacement that had about 90K miles on it when I got it about 18 mos. ago. I do local and highway driving to go to work. Will I damage the engine if I don't have it fixed?

My car has 185000 miles.
My car has an automatic transmission.