Most major companies have been pretty far behind in terms of BTC development. The
vast majority of recent transactions have still been legacy transactions rather than SegWit transactions, and most of the major services have not implemented SegWit yet despite the fact that there have been relatively stable releases in TREZOR and a couple of other wallets which
have implemented it.
The Lightning Network may take an even longer time.
Implementing Segwit doesn't take much developer resources, according to most developers. Companies like Coinbase and Blockchain.info not implementing Segwit is more of a political statement than anything. It should also be noted that Segwit alone doesn't bring that much benefit (only ~2x in fee savings).
It's the post-Segwit features and infrastructure that are really ground-breaking, and those take time to develop. Once the Lightning Network is working on mainnet, there is
much more incentive for services to integrate LN payments for their customers. The fee savings will be great enough that I believe users will definitely default to exchanges/payment processors/merchants that support the Lightning Network. Notably, Blockchain.info has an LN implementation (Thunder).
I doubt that we'll be seeing the full effects of the Lightning Network until a year or two from now, and by then this bull market is fairly likely to have subsided.
I agree that it'll probably still be a year or more before LN starts seeing noteworthy transaction volume. There are lots kinks to work out and there is no software available yet for end users. As for price? This rally will have subsided by then, but I'm doubtful that the bull market will be done with.