Pretty much echoing what Omar has already said! The lattice is a great way to non-destructively manipulate the geometry without having to edit the underlying vertices. This could be a great way to inflate the sides of the tire as well, keeping in mind that you may need some more slices on your lattice for more granular results.
To the second part of your question, the main reason I went with modeling out the sides of the tire in our base mesh was because it allowed us to easily model in features to the sides of the tire, such as that circular cut that we do into the Tractor Tire episode. This is an area that may be harder to achieve by using the lattice, thus why I opted for something more manual. The lattice would start to get overly complex if we wanted to start adding designs or patterns into the side of the tire that actually cut inwards on the tire.
Ultimately it’s a game of trade-offs when working in 3D. For me, the lattice was a great option to easily push out the silhouette of the tire but would’ve quickly over-complicated those other design aspects. 🙂