It depends on what you meant about the connection or what you want to do.
I managed to create a simple chatting program that allow me to send messages between my Android phone and computer via WiFi of the same network. It works as what I want. I'm planning to improve it further to allow me to connect my mobile phone and remote computer over WAN. It is much more technical, it requires ip forwarding, etc. But I'm not familiar with those thing. But I have an idea that allow me to bypass that technical issue, by using a web space that put between them so they (the phone and computer) can communicate using it.
I also have tested the capability of Lazarus to make Android games. Yes, I managed to do it. Recently, I've purchased my first Arduino + Raspberry learning kit. Now I'm still busy with my job, maybe next month I will have time to explore how to connect between Ardunio/Raspberry, Android phone and computer.
Lazarus has endless possibilities. Some users here use Lazarus to create app and put it on Play Store. Android programming in Lazarus is powerful, you have all the tools you need. Unfortunately the tutorials/documentations are hard to find, we have to search the information from other sources.