For starters, let's look at how adults could relate to the film in order for them to enjoy it. Throughout the film, we see the main antagonist, Lord Business, boss and shout everyone around. This would relate to most of the adults as there is most likely one person at work who likes to boss everyone around. Looking at his character Lord Business clearly resembles an adult dealing with children messing around, as he wants things to be "perfect". This would relate to parents who are finding their children a struggle to deal with, so in return, they may support Lord Business as they feel like they are in the same position as he is in, "having to clear up the mess".
The child viewers may relate to the protagonists (the master builders) as usually, parents ruin all the fun. Some children may relate directly to Emmet (the main character) as he doesn't seem to fit into his society. The film may draw children into watching it purely because most children love LEGO as I can personally relate to as a lot of my younger days of my life were spent playing with LEGO.