Yes, it certainly will. As it happened with SegWit and LN MWEB was invented long before, ans proposed for PoW blockchains (BTC and LTC), but developers decided to implement it earlier in LTC with Charlie Lee being one the most enthusiastic proponents in both cases, but with the involvement of developers of both blockchains. The cool thing is that once something new is developed and/or activated in one of the two, the implementation on the other is faster, sine they are so similar. Taproot was developed for BTC, while MWEB was for LTC first, and now LTC will activate taproot. and BTC will MWEB later, for sure.