There's no new syntax for exception handling in lambdas. Exceptions thrown in a lambda are propagated to the caller, just as you'd expect with a regular method call. There's nothing special about calling lambdas or handling their exceptions.
However, there are some subtleties that you need to be aware of. Firstly, as a caller of a lambda, you are potentially unaware of what exceptions might be thrown, if any and secondly, as the author of a lambda, you're potentially unaware what context your lambda will be run in.
When you create a lambda, you typically give up responsibility of how that lambda will be executed to the method that you pass it to. For all you know, your lambda may be run in parallel or at some point in the future and so any exception you throw may not get handled as you might expect. You can't rely on exception handling as a way to control your program's flow.
To demonstrate this, lets write some code to call two things, one after the other. We'll use Runnable...