A mild LCL injury or sprain will take about 4-6 weeks of conservative treatment to heal. Even then, you should continue to stimulate blood flow to ensure complete healing and to prevent re-injury.
A moderate LCL tear will take about 2 months to fully heal. At the 2 month mark you should be able to resume most of your regular activities.
A complete LCL tear will take 3+ months to heal, with the aid of surgery.
While most people who have recovered from an LCL tear should be able to resume all of their usual activities eventually, some people will never regain the same stability and strength their knee had previously.
It is recommended that when you are recovering from an LCL tear, you gradually work your way back to your former activity level. If you are used to doing high intensity workouts or exercise, start with something more low-impact. For example, if you are a cyclist, start with something like water aerobics, then move onto using a stationary bike once you've built up more strength and accomplished more healing. Eventually, you should be ready to start cycling regularly again.
If you are recovering from LCL surgery, you may be required to wear a cast or brace for several weeks, in order to keep the weight off your tender knee. You will also have to use crutches to help you get around while your knee heals.