I know that the usual policy is to tier Pokemon based on how much they contribute over the whole run, but if you instead view it from the perspective of "should I use this Pokemon when I do obtain it", then for Lugia the answer is probably yes. It's the bulkiest Shadow Pokemon, it's the least likely to enter reverse mode, and unlike Snorlax, it gets good Shadow moves. I'm pretty sure that the game expects you to use your Master Ball on this, so I wouldn't count the 5-slot thing against it. The fact that it does measly damage is a good thing (if you're planning to capture all the Shadow Pokemon), but if you need to chip down enemies faster, you can use Shadow Down with a physical Shadow partner. This is not an F tier Pokemon. In fact, having a role this significant in an efficient playthrough means that it's also probably too good for E. Salamence is better though.
I'm also going to give impressions on the Pokemon I used over the whole playthrough; since it was my first run, I mostly stuck with Pokemon that are actually good.
Espeon - Basically, the in-game Kadabra experience. Light Screen was helpful at times. No complaints. But it definitely does need the Psychic TM.
Teddiursa - If the only move it ever learned was Return, I would rate it exactly the same. With a Choice Band it OHKOes everything, and without a Choice Band it still usually does. Although I may dock some points because during certain parts of the game, that's not what you want. I gave it Brick Break and I kind of regret it, it would have benefitted Breloom or Medicham a lot more.
Houndour - Fire Blast was the strongest nuke on my team for most of the game. Charm is surprisingly useful, though Arcanine made better use of it (more on that later).
Shroomish - You definitely feel Shroomish's lack of offensive presence before it gets Headbutt. And you definitely feel Mach Punch's lack of power against Normal-types that aren't complete wimps. Nonetheless, 130 base attack at lv23 is pretty stupid. Breloom was very helpful in the purification chamber, and I decided to leave it there not because I was unsatisfied with its combat, but because I use Breloom in playthroughs too much.
Carvanha - I ended up not using this in the long term because there aren't that many Water-weak targets, Water Pulse is not that strong to begin with, and Rough Skin is a liability. But the Carvanha stage was not that bad to be honest, with comparable bulk to Houndour.
Meditite - obtained slightly late, but caught up easily. I kept Dynamicpunch on the moveset because I thought it was funny. Since Ursaring got Brick Break, I ran HJK on Medicham. Using its main STAB made me nervous so I used it less often than my other members, but it was able to keep up anyways because of trade EXP.
Zaprong - the enemies are so bad that Zaprong itself might as well not have a dud stage (unless you count Togepi as a dud stage, but that's functionally identical to snagging a Shadow Elekid and purifying it in the chamber). Insane speed. Insane coverage. Insane growth. Not much utility apart from the occasional Thunder paralysis. Probably the best non-Shadow Pokemon on my team.
Growlithe - Ran its starting moveset for the entire game. It was basically Houndoom with better utility, including Charm. I would usually lead with this; in difficult fights I could often cheese physical attackers by dropping them to -3 and then doubling up on the other slot, which turned battles into 2v1s. And yes, I ran with two Fire-type dog Pokemon.
Shadow Snorlax - functioned identically to the roadblock Snorlax in Kanto; I used it on my team for the sole purpose of sitting there and doing nothing while Shadow moves bounced off of it. I would not recommend actually commanding Snorlax to attack; it is better to just waste a turn with Call and hope the enemy uses Shadow End on you. In the final battle, Snorlax got trapped and I needed to bring in Arcanine to spam Charm on Exeggutor, so I had to KO it with my own Lugia to do so. A roadblock all the way to the bitter end. o7
Shadow Electabuzz - brought exclusively to use Shadow Half. I deliberated between using this or Shadow Swellow, but in the end I don't think it mattered considering how little I ended up actually using Shadow Half. Shadow Storm was fine, usually doing like 30-40%.