Whether dividend re-investment in a Tax Saver fund also subject to a lock-in period of 3 years?

The answer is Yes.
 Any investment made into an Equity Linked Saving Scheme (ELSS) is subject to a lock-in period of 3 years. This holds good even for dividends from ELSS which is re-invested if the investor has chosen the dividend re-investment option.

The implication for the investor is that some portion of his investment will always be locked-in because dividend declared is re-invested and will attract a three year lock-in. However, any portion of the investment, whether originally made or as a result of dividend re-invested, which has completed the lock-in period of three years, can be redeemed by the investor.

So in such situation in order to avoid lock in period of 3 years in dividend which is reinvested, best is switch to dividend payout option.