Just raising the block size was a simple and elegant solution that could have avoided a contentious hard fork
Evidently not. The option to hardfork to a larger blocksize was freely available, but not enough people chose to go with it. The majority decided that a softfork to an opt-in 4MB blockweight with SegWit and Lightning was a more sensible option. Plus, it's arguable that one hardfork to increase the size wouldn't be enough and future hardforks would likely be required.
The Lightning Network is a "second tier" payment protocol that operates on blockchain (most often Bitcoin). It allows instant transactions between participating nodes and has been touted as a solution to bitcoin scalability issues.
People often describe it as "second tier", but in the big picture, I tend to think of it more as "inter-tier". It will effectively weave any future tiers together and allow you to move your funds between them.