When I was working in studios we always put exposed film in the plastic bags in emptied film boxes for pick-up and delivery. Rubber-band (use two) or tape the film box to prevent disasters. Even with 100+ holders, we shot enough that we needed to cycle film through them faster than the processing cycle, especially over a weekend when labs were closed. This was all E-6 and studio lighting, so the top sheet was processed and inspected for any necessary push-pull adjustment, then the rest run at the chosen adjusted development.
I wouldn't give film holders to a typical lab because of the danger of mis-handling or loss. If someone drops holders, a light leak could result and ruin your next great shot before you find out. If you don't yet have an empty film box and bag, ask the lab for one in good shape. If you do trust the lab completely, and it's small and carefully run, you might give them holders if you have plenty to keep you stocked while some sit at the lab. Mark them clearly, obviously, and permanently as yours.