There is no way that CoinBase would have added LTC without SW.
so charlie Lee working at coinbase has nothing to do with it.
Obviously it helps, but without segwit LTC would have no selling point. Who wants a BTC clone with prospects to get anything new done? that was LTC before segwit. In this post-segwit reality, LTC can shine to unforeseen prices thanks to what segwit being activated means, this creates a big bullish pressure that Coinbase can cater for.
But of course, anti segwit FUDsters will never admit segwit drives the value of a coin up objectively speaking.