It is possible. Unfortunately, what you seek is not something that can be done without any manner of programming. Basically, your goal is that List A Column 2 is a Lookup column that references a specific value on List B. This itself is simple enough, just create a Lookup Column that references said value on List B.
To make it specifically grab the List B item whose Column 1 value is the same as the Column 1 value on the List A item, that is what will require some amount of code. Be it an Event Handler, or maybe you could set up a workflow with SharePoint Designer (I'm hesitant about that but I imagine it should be possible to some degree). It is not that difficult of a code and I can provide you some basic instructions to set it up if you wish to go down the programming route.