The very first thing I will say as a huge LAM fan and someone who uses them frequently: be patient. The movement rules can be unforgiving to LAMs so don't sacrifice your movement modifier just so you can attack every turn. Attack when you have the advantage. This doesn't mean you have to have won initiative, just be sure when you do commit that you're moving for best modifier on a target that's vulnerable (low defensive modifier, can't shoot back, really thin/breached armor).
Second, know that LAMs perform best in campaign setups. It has been said to death because it is true: LAMs are a strategic tool. If you can plunk a single Wasp LAM down on a supply depot being defended by a company of plain-Jane rifle infantry, then that's where that Wasp LAM belongs. There are a whole host of things that go into using LAMs in a campaign setting, forking attacks, recon sorties, strategic maneuvering, etc., etc.
Third, if you are using LAMs in a one-off scenario, don't expect them to punch at their weight. Heck, don't necessarily expect them to punch. Use them to corral the enemy by threatening backshots, or as spotters for indirect fire, or go to fighter mode to make the enemy waste units pointing at the sky instead of at the ground. There are a ton of things LAMs are great for but shooting at stuff isn't really their forte.
Fourth, LAMs are most fun for both sides in scenario based games. While it can be great fun for everyone to just smash 'mechs together for an evening LAMs high hit mods and low firepower don't tend to accentuate this. But an extraction or smash-and-grab scenario? That's where LAMs can be fun for all. That scenario I mentioned with the Wasp LAM against the PBI above? That was one I actually played and it was great. The PBI weren't trying to kill my LAM, their objective was to get away with a very specific VIP that I didn't know was there. My objective, of course, was to blow up supplies. Once I realized there was something even more valuable there then I had to decide if risking the PBIs was worth it. (FYI I took the gamble early on and lost the scenario.)
As for specific tactics: If you're going to use airmech mode, I always recommend ending a LAMs movememt pointed directly at an enemy, ideally in the rear arc. Makes them weigh carefully just how badly they want that annoying thing off the field and if it's worth a potentially devastating charge against their own unit.
Also, always try to give the enemy someone else to shoot at. LAMs just aren't that hard to kill so if the enemy has to decide on swatting at that Stinger LAM or getting started on the Warhammer over there your Stinger might be able to indirectly use the Wammy's armour for a turn.
To be courteous to your opponent please try to plot out your LAM movement ahead of time. The turn mode rules are a bit combersome as they are based on how many MP you're spending but you have to know where you're able to turn to know how many MP you're spending. It's little fun for anyone to spend twenty minutes trying to juggle the math on that so cutting down on your opponent's perception of that can help the game be more enjoyable.
