I want to connect two private lans each of which have two routers with one each serving as an access point. Each of these lans have their own internet connections. I want to share files and setup gaming between these two lans without sharing their internet connections. The first lan is in the ground floor of my building while I live on the second floor. I just want to be able to share files and game with my neighbours without sharing my internet connection
If you have no overlapping IP addresses you should be able to use a router to connect the networks. Your current ones may or may not have the correct features.
The simplest way is to use router that you can run dd-wrt on which will then let you have multiple wan and lan interfaces. This allows you to connect the networks together. The internet is actually tricky to share and by default the networks only know their own default route. You can of course in the router that connects the 2 networks put in rules that prevent it if the users got creative.