Yes, but the solution landscape to this problem domain is different. Automatic variables have well-defined lifetimes; they die when they go out of scope. This means there's greater scope for the compiler to take more initiative about lifetime of captured variables (which will all be automatic one way or another, i.e. implicit 'this', a local or a parameter; assume reference parameters etc. cannot be captured).
When I designed and implemented the same feature, anonymous methods in Delphi, I used reference counting to keep alive a heap-allocated activation record containing all captured variables. This works well for most scenarios; it can get into knots in more obscure situations where you have recursive lambdas that call themselves via a captured variable, but those are usually pretty rare.
You're right that GC is a help. The biggest thing GC gives you is freedom from having to worry about who controls the lifetime of parameters and function return values, in most cases. In the presence of GC, you can get more clever about your algorithms and data structures; you can cache and memoize, without paranoid concern for things disappearing behind your back. Consider a querying API that takes in closures for sorting and selection functions; I can see it building up temporary results and caching them, or streaming results in a multi-threaded fashion, but it can only do that if it can reliably hang on to closures after the select/sort/etc. function has returned.
