What's the technical problem with Lightning? What is making the exchanges hesitant from integrating it to complement their service? Plus are there business development people behind Lightning Labs to handle onboarding the exchanges and other institutions?
Aside from what @jackg said and classical problem such as "why bother upgrade if it's not broken" or "the code is poorly written/have no proper documentation", there are few specific concern (both technical and non-technical) such as :
1. What happen when a channel is closed, but the used on-chain transaction fee is low and there are many pending transaction on mempool?
2. Most LN implementation (e.g. LND and c-lightning) are still on beta, which isn't acceptable for most exchange and writing their own LN implementation isn't an option for smaller exchange.
3. Educating customer who don't know their LN wallet doesn't accept incoming transaction