Yes, that's how you pick lettuce. Just the biggest leaves. I don't strip mine all the way down unless they are ready to pick. There will be plenty of young leaves so I doubt it will all be ready at one time on each plant.
My favorite is black seeded simpson.
If you want to start your lettuce super early, you can built a lid and cover with plastic. I'm getting ready to plant mine this month. It may not grow much, but it will at least germinated.
And I always have first lettuce here where I live. You can water it from time to time also. Don't make the topper too heavy. It's hard to lift off.