Pulling some 'Mechs out of the Cache, eh? I can work with that.
I'm going to categorize your 'Mechs in two different ways, through potential and endurance. Potential signifies how amazing the unit can be when given optimal conditions, while endurance represents how long those optimal conditions usually last.
EXC-B2 Excalibur-- High potential, low-medium endurance: The epitome of run-'n-gun. It's almost like the design of the 'Mech dictates the only way it can be used. Move around, get good movement mods, demolish things at range, get hit, die. Ammo dependency and armor are obvious issues; intervening terrain is the unknown factor that can nerf the effectiveness of its weapons. Amazing with enhanced Gunnery pilots.
ST-8A Shootist -- High potential, low endurance: I love the Shootist. It's such a great 'Mech. But let's be honest, it's a super-Hunchback, and we field it for the AC/20. And there are only 10 shots, less if you take 1 or 2 tons of specialized ammo. If the ammo runs dry or the AC takes a critical hit, the Shootist becomes a slow rock with a few dinky energy weapons. Absolutely make sure you place this 'Mech on the right side of your starting position, and expose only your right side in your approach to the target. It may be fluffed as a bodyguard, but this 'Mech is the juiciest target of the lance.
BL-6-KNT Black Knight -- Moderate potential, high endurance: You know, I think the original Black Knight is cool because it wasn't horribly min-maxed like the stuff you see in TRO 3058. 20 Single Heat Sinks means all those lasers are redundant weaponry. It also means that this 'Mech has a very forgiving learning curve and is great for beginners! But I digress. This 'Mech is clearly a brawler, but with an additional option to completely mutilate a target with an Alpha Strike at the risk of bad heat modifiers and shutdown.
SPT-N2 Spartan -- Low potential, moderate endurance: It's weird! It's got an XL Engine! It's got too much ammo! It's got too much un-CASE'd ammo! But the absolute best thing that the Spartan has going for it is that it has the weaponry of a Medium 'Mech! Nobody will shoot at it...It's actually a bodyguard 'Mech! That is, until the TAG hits.
Lance Tactics
3 Heavies and an Assault. All designed for anti-armor work. Not really a lance that pulls any punches. It really has two modes: "extremely blunt instrument" mode and "mop up broken ranks" mode. Start by placing on the right side of your starting area and cross the map diagonally, turning to zigzag when needed. The Black Knight should be running out in the open, looking to draw attention with its PPC and a Large Laser. It is the anchor of the lance, and not many will argue about that.
The Shootist should stick close to the BLK, finding cover when possible while jabbing with its ERLL. Pamper it like a princess, because its purpose is not fulfilled yet.
If the Excalibur out-ranges the enemy on average, let it run the flank to keep its flexibility up as much as possible. The opposition will likely need to roll quite high to hit it during the approach anyways. If the Excalibur does NOT have the advantage (or if your initiative looks bad), it should be looking for cover like a fish for water. Depending on how good its Gunner is, the 'Mech will occsionally need to stop in order to get a decent to-hit number at range. Also, depending on how long you estimate the scenario will be, the EXC may even have to hold off on the LRMs to save ammo. However, all of these special actions carry great risk with them, but that's really what the 'Mech's all about.
The Spartan is the wild card here. It can either run ahead of the Black Knight to get ready to start brawling and TAGging things, or it can be reserved in the middle of the pack to keep its endurance up for later. Essentially, it is your replacement Black Knight, unless you have artillery, in which case it becomes more valuable than the BLK.
IN THE MIDDLE OF THE GRINDER? That's when the fun starts. Exactly TWO turns after your Shootist gets within range to start delivering its real payload, your Black Knight will fire all of its weapons in an Alpha Strike. I kid you not, sir, I can see the future. That is the optimal time for the BLK to start working on crippling units rather than damaging them. At the same time, the Excalibur needs to break off from the group, flank the area of contact, and either go for backshots or cover the opposition's escape. You can start using it at the optimal 7-hex range from your targets now, because at this point it's do or die. Get the Spartan next to targets and work them over with ALL your weapons, and 16-point kicks. There's no sense in playing an 80-ton 'Mech conservatively if you've been saving it up for this point. With the dice on your side, enough power delivered in one turn can make the rest of the battle much easier, much like how taking the effort to cook meat before it spoils is a good idea.
Conclusion: Big armor and big guns will get used for big brawls. Timing each 'Mech's Moment of Glory is what will count the most, however.
Special Situations and Equipment
WHAT TO DO IF YOU LOSE YOUR AC/20: It's not all bad yet. Though the conflict for you will now likely last quite a bit longer, the focus now is the at least make something of your lance's weight. Keep focusing on the heavy enemy units that are in the way of you taking a vital position, because that's the least your Standard Fusion Engine 'Mechs can do. Stay in a tight formation to ensure all of your brawlers' weapons and physical attacks can hit the same target. Pulse lasers, punch, kick, charge, play rugby, do whatever it takes to make sure the OpFor stays on the ground as much as possible. Keep running the Excalibur the way it's always been, or if you feel it's too valuable, let it hang back to take a break. ---- Conclusion #2: Once your 'Mechs' potentials have run out, it's up to their endurance to carry the day.
Setting up ambushes and getting ambushed: Make your Point-Blank attacks, then go immediately into "mop-up" mode. The enemy has basically done the work of getting close for you.
Artillery: TAG with the Spartan. Hit things with Arrow IV Homing Missiles from offboard. If allowed, follow up with Semi-Guided LRMs from the Excalibur. Rejoice.