After using Delphi for a long time (starting with TP1), I switched to Lazarus and have been very happy with the decision. Delphi has become, in my view, an excellent tool for the professional programming team, while Lazarus seems friendlier to amateurs (like me!).
There are certainly differences, but I have been able to convert all of my Delphi programs to Lazarus without too much effort. The conversions have been a good way to learn to use Free Pascal and Lazarus.
The difficulty with using networks in Lazarus will depend at least 80% on how good your basic knowledge of networking is. I'd look for tutorials about networking in general (for the OS you're using) on the internet first. There are quite a few, and they will give you the background you'll need to understand networking with Object Pascal / Free Pascal AND Delphi.