Retail lots - are they owned by a Sim or by the Household?

When you split the household just make sure the sim(s) you want to own it stay(s) in the left-hand pane (original household) and any other sims go in the right-hand pane (new homeless household, automatically marked as played/favourited).

Once you have done that, you can move the sims between lots as necessary.

Doing it this way retains any Perks that would get lost when selling and rebuying.