Those look wonderful! I like how you went with recesses instead of notches too.
If these are going to be "used as intended", then I'd recommend a nice beeswax or food safe oil finish on them. If they are going to be more for "decorative" purposes, then I also agree with the lacquer. Mesquite and walnut arent particularly soft and are highly durable on their own anyway, maybe no finish would allow them to develop a love patina of use over time? A simple coat of paste wax might be good enough here.