It doesn't increase lift. It does pitch the nose up (increased angle of attack). That's how you compensate for dropping (loss of altitude) from reduced lift. Mind you, increasing the angle of attack increases your stall speed... so make sure you have adequate speed to keep from stalling (and falling out of the air.)

Anticipating your next question ("What do you do when a stall occurs?" ) the answer is, pitch the nose down, so you gain air speed over the wing, level the wings, and recover to level flight. Then recover your altitude. Then try your turn again, with additional air speed.

Which will generate more questions. It goes on, and on, and on. Enjoy!
Dave Olson