Let's let it segwit go live on LTC first. Right now it has never been tested on a network that has actual value. That should be a minimum requirement before we implement such a major change on the bitcoin network.
Unfortunately LTC has on actual economic value rather than a speculative one. Its main differentiation points, namely being ASIC resistant and having a higher txn throughput are both pretty moot. The former is not valid anymore (ASIC HW for scrypt have been developed and deployed for years), the latter is moot because ltc blocks are pretty empty.
As you can see there's no actual demand for ltc transactions, hence no economic value rather then the speculative one.
That said testing it on the LTC mainnet is for sure a step forward in respect to testing on bitcoin various test nets.