Lower body liquid iron.

How does one strengthen their ligaments, and tendons in their lower body?

By subjecting their bones and muscles to load and force. I'm sure you can work on your connective tissue with specific repetition schemes or TimeUnderTension.

This can be merely running and jumping. Walking does this to some degree as would hiking and rucking.

Of course, lunges and all types of single leg squats or various barbell movements such as but not limited to the squat and deadlift will do.