Just do the lat pulldown machine. Nothing wrong with it. Even when i could do 30 chin ups @ 215 lbs bodyweight i still used the pull down machine most of the time. The whole stack wasn't heavy enough for me, but i would simply hang a 25 pound plate on the pin ( which was probably a really bad idea and dangerous ). I would sometimes do real Chin Ups just for the cool factor, both with bodyweight and with added weights but the pulldown machine was always my staple - i preferred it for training, and used the real chin ups mostly to test my strength.
You can use different form both on real chin up and on pulldown machine - it's not what equipment you use in this case, but how you use it. the technique is going to be different on the machine vs real chin ups but the muscles targeted will be mostly the same depending on what form you use. If you cheat a lot the difference between machine and chin up will be large, but if you use strict form it will be small.
the advantage of the machine is you can dial in the exact resistance level. once you get strong enough you will be able to do the same with regular chin ups using weight belt or holding a dumbbell with your knees, but even so the machine is still going to be better for quick weight adjustments, drop sets etc.