Which GoF Design pattern will be changed or influenced by the introduction of lambdas in Java8?

I think your will see the most changes in Behavioral patterns.

Template Method - Template methods will be more and more seldomly used, and instead we will see objects pass functions to the AbstractTemplate instead of subclassing the AbstractTemplate. I blogged about this a loooong time ago here: http://hamletdarcy.blogspot.ch/2007/11/groovy-closures-end-of-template-method.html

Observer Pattern - Observer becomes simplified because you no longer need to keep a list of observers that get updated on new events, but instead keep a list of functions that need to be called back on new events. So there is no more Observer interface and just function objects.

State/Strategy Pattern - I group these together because they are structurally equivalent, just different in intent. Strategy usage become much more common because it is easier to implement. You don't need a parent strategy and strategy subclasses, you just need functions. So it is simple to just pass a function as a parameter, which in effect is using the strategy pattern.

Overall, I think any pattern that requires a one-method interface becomes easier to implement. This will have the two effects. 1) We will use these functional patterns more, and 2) we will stop referring to them as patterns but just as "passing a function".

You do what you want, but I think "JavaScript the Good Parts" gives a pretty nice introduction to leveraging functions in a language. You might pick it up and read it!

I tried to reply to this question myself writing a series of articles where I analyzed some GoF pattern and their functional counterpart with practical code examples. In particular I revisited: Command and Strategy, Template and Observer, Decorator and Chain of Responsibility, Interpreter and Visitor.