If The LEGO Movie 3 happens, I wouldn’t be surprised if it took a Toy Story 3-like approach and showed Finn either packing up his LEGO upon reaching adulthood or, if they wanted to go even further into the future, show him playing with his and his dad’s LEGO collection with his own child.
None of this is to say that the LEGO movies are better than the Toy Story movies overall.
Nevertheless, because The LEGO Movie and The LEGO Movie 2: The Second Part opted to take a different approach with the relationship between toys and their human owners, the result is that what goes down in the LEGO-verse echoes what happens in real life, which is the point.
In fact, in the grand scheme of animation history, the Toy Story series is likely to held in higher esteem, from how Toy Story was the first feature-length computer animated to how Toy Story 3 raked in numerous accolades and over $1 billion worldwide.