Hey Javi, how are you? I hope you are doing just fine!
I shall provide you with an explanation of the usage of the word ''get'' in the context concerned:
1) Firstly, you should know that you use ''get to'' or ''grow to'' in front of another verb to say that someone 'gradually starts to have a particular attitude or feeling'. The idiom ''grow to'' is more formal than ''get to''.
E.g.: ''I got to like the idea after a while''.
E.g.: ''I grew to dislike working along with him''.
* You also use ''get to'' to say that someone 'gradually starts to know or realize something'.
E.g.: ''I got to understand it more as I grew older.''
E.g.: ''You'll enjoy college when you get to know a few people''.
* If you ''get to do'' (something), then you 'have the opportunity to do it'.
E.g.: ''They get to stay in nice hotels''.
E.g.: ''We don't get to see each other very often''.
As regards your example ''I get to go away another time if I am lucky'', the idea conveyed is that you can have the opportunity/be able to leave (a certain place) or depart, or even travel to somewhere in particular (another time) if you are lucky.
Did you get the idea? I hope you did! :)