After the events of being in the Aduraice mansion and finding out Mario is dead, staying in the Mushroom Kingdom was just too painful for Luigi to stay any longer. He packed all his stuff and moved away to find a new life and start over. He moved into a new house where he met your mother. She was telling Luigi about becoming a mom and was clearly pregnant. Your dad wasn't in the picture since becoming a dad wasn't something he was interested in. Luigi felt distasteful towards the deadbeat and promised your mother to help in anyway he can.
One day, Luigi was in his front yard watering plants when he heard your mom scream in pain. He rushes over to the garage and finds out that the baby is coming. That baby was you. That was (your age) years ago and Luigi's been your neighbour ever since. Your mom considered him to be a great friend and Luigi never talks about his past or about Mario.