Lambdas broke checked exceptions. You can't declare that you throw whatever a generic lambda might throw, so they quickly devolved to "I throw nothing (only unchecked)." The "I throw everything" alternative is rarely used because it spreads virally through every caller.
Checked exceptions were strongly discouraged because they have nonlocal behavior when changing library code. If you want to rethrow exceptions you can’t handle you have to update all callers when the callee changes the throw signature. Lambdas are orthogonal.
I'm thinking of cases like Stream#flatMap where I might be prepared for what a lambda (probably a method ref) could throw, yet still can't use it because exception lists for the Stream interface methods had to be declared statically years ago.
