If you can get something close enough to kick a leg, there's not a lot of armor protecting it, and it's easy enough to keep it on the ground until the pilot surrenders, or your infantry shows up to drag him out of the cockpit. A one-legged Stinger LAM is probably repairable without too much parts-hunting, and still valuable. If you have to shoot it repeatedly, you run the risk of coring it, and reducing it to spare parts.
Since nothing ever goes entirely according to plan, I'd probably opt for a Plan A to infiltrate a sniper into effective range of the enemy compound, to pick off the LAM pilot on his way to the machine. Plan B would be to have an extremely fast 'Mech race directly toward the LAM, and try to get to it before the pilot arrives, or at the very least, before he can get it airborne. Depending on the success/failure of the sniper, the attacking 'Mech can either target the pilot or kick the still-inactive LAM over, doing leg damage and delaying its takeoff until it stands up again, during which time you're kicking it again. The problem is getting your sniper in place without detection, and getting a 'Mech close enough to make the sudden dash before the defenders can mobilize. That means using terrain, weather, and possibly active sensor jamming to get close enough. Your main force will arrive somewhat later, so that initial attacker needs to withstand whatever the defenders can throw at it until the LAM is down or the rest of the attack force arrives. If your group has access to a Jenner or Ostscout (7/11 or 8/12 movement and enough mass to do decent kick damage), that would help, although a standard Locust could probably pull it off almost as well.