The hashrate for segwit right now is past 97%, which is ironic since it's higher than the 95% required for BTC.
Even if Bitcoin never gets SegWit it'll have value as an immutable asset. It's just easier to transition into SegWit on Litecoin because there's still less money (and let's be honest, corruption and monopolisation) in Litecoin than Bitcoin, but this will change.
When the fees on bitcoin are so high that you cannot properly make payments that aren't bigger than this high fee, you better believe that Litecoin with SegWit and Lightning Network will continue going up since the use of it as an actual tool to make payments is viable. BTC will end up as a hodlers coin like gold with barely any transactions (who wants to pay for example, a subscription to a website while paying $1 fee or higher, when you have LTC?)
But BTC always will get updated faster since LTC just copies Core's code, but will benefit from activating segwit from said updates in a better way.