Technically, Segwit was not necessary for the Lightning Network to work. It's just that all Lightning Network code was built with Segwit's transaction malleability fix in mind. So, as coded, we need Segwit. I think we will start to see Lightning transactions on the mainnet next year but I don't want to be overly optimistic about the timeline for full adoption. The routing and network topography issues are still not completely sorted out and tested.

The other thing that we need to come to terms with is that on-chain fee should and will continue to rise, regardless of the Lightning Network. Even if LN eventually takes a majority of network transactions, that suggests exponential network growth, and every channel requires two on-chain transactions (to open and close a channel).

Thus, demand will remain high for limited on-chain transaction space. At the same time, we need this demand to push fees higher, because transaction fees need to pay for the network's security. As each reward halving goes by, it becomes increasingly important that fees rise to replace the block subsidy that is disappearing.