I have two reference questions

1. What should be required of a category with finite products so  that a (multi-sorted, finitary) Lawvere theory induces a monadic adjunction on it? This should be perfectly standard (I think I saw it a month ago), but now I can't find it in books, nlab or MO.

2. What should be required from a model category so that the category of algebras of a (multi-sorted, finitary) Lawvere theory in it has the right-transferred model structure?