Finally was able to solo MACHAMP
I'm here just to share my experience and show my disappointment with Lugia.
It took me 3 times to win, and the first two ones I've put Lugia in the last position to avoid losing all of my mons. I can't disagree that he is a perfect pokemon to receive damage, but on the other hand is a TERRIBLE attacker. My lugia is a 98% with E/Fs and 3070 Cp.
My team of the first 2 attempts was:
Exeggcutor 98 - Es/So - lvl 30
Exeggcutor 96 - C/Sb - lvl 30
Dragonite 98 - Dt/Hu - lvl 30
Dragonite 96 - Dt/Hu - lvl 34
Alakzam - 86 - Ps/Fs - lvl 30
Lugia 98 - E/Fs - lvl 30
Success Attempt
Dragonite 98 - Dt/Hu - lvl 30
Dragonite 96 - Dt/Hu - lvl 34
Dragonite 98 - Dt/O - lvl 34
Dragonite 98 - Dt/O - lvl 34
Alakazam 86 - Pc/Fs - lvl 30
Alakazam 75 - Pc/Fs - lvl 27
Answers
Using the Dodge Special Pro simulation with either E/SA or E/FS, you should be able to do it with level 36+ vs C/CC. But both would be by the skin of your teeth. Higher level would probably give you slightly more cushion.
https://www.pokebattler.com/fights/attackers/LUGIA/quickMoves/EXTRASENSORY_FAST/cinMoves/SKY_ATTACK/cp/3392/defenders/MACHAMP/quickMoves/COUNTER_FAST/cinMoves/CLOSE_COMBAT/cp/18144/strategies/DODGE_SPECIALS/DEFENSE_RANDOM_MC?includeDetails=true&seed=1504229912062
That's why Lugia is listed as superior counter against Machamp, huh?
Exeggutor/Espeon/Alakazam can fire off 1-2 charge moves if lucky. Lugia can use FS many more times, which in itself not a big deal, but charges up faster by taking the hits, so you actually gain time here. It happened to me several times, that Alakazam came in, got hit by the charge move and fainted straight away. Dragonite may be 40% stronger, but does not do SE with Dragon Tail, so damage is roughly the same. Solar Beam looks superior with 180 damage, but if you consider SE on Future Sight (120*1.4=168), the difference is not that huge, even if you consider that Exeggutor is only 20% stronger than Lugia.
Lugia: Lower DPS? Yes. Useless for Machamp raid? No.
Probably that extra alakazam I'm guessing. I always start with my two alakazams when soloing machamp. If I dodge 2-4 charge moves I know I'm home and continue. If i don't I know I will time out so I just restart.
I don't know what battle order is the best but it's really annoying wasting time and dodge miss 2 charge moves in the end so I prefer having my glass cannons up front; after (I'm guessing) 40 seconds you know if you will make it.
I beg to differ. Lugia with ES/FS is the difference between an uncertain fight and a comfortable victory. Save your Eggies for Vaporeon and focus on Espeon and Alakazam. The team below has only lost one out of approximately 20 fights against any move type. That was when one of the Espeons didn't manage even a single FS. If anyone of the first four manages more than one FS the fight is over with more than 30 secs left. No need for dodging. Before Lugia I wasn't even close against HS and DP (with a Dnite/Hu lvl 30,5).
If im reading this correctly, you timed out on the first two attempts. Your team is plenty adequate, so I'm guessing your phone or cell service might be a factor. How much time is on the clock when you load in? Before my phone upgrade, I could lose up to 15 seconds (usually around 8) which is a big deal against a tough move set.
I powered up my lugia to over 3k CP and Machamps no longer pose much of a challenge. So I'm going to respectfully disagree on that point. However, I'm using Sky Attack but I still don't think that's the issue. I also prefer to anchor with Lugia so I can just unload with my glass cannons. I no longer use Eggs either. I lead off with 3 espeons, followed by Alakazam, Dragonite, Lugia. Against double fight moves, I'll use my best Gengar to lead off and kick my alakazam.
I think my team is worse than yours and I'm able to consistently solo Machamp with any moveset, with about 10-15 seconds remaining. Sometimes I don't get to my 6th Pokemon either.
In order, my team is:
Alakazam C/F level 31
Alakazam C/P level 30
Exeggutor E/SO level 30
Gengar H/SH level 30
Lugia E/S level 30
Dragonite T/O level 30
I used to use the Dragonite before Lugia but it didn't make a difference, I was winning in about the same time so it was just costing an extra revive and potions, it's just filler as I don't have any other specialists.
If your lineup is also in order that you used your Pokemon, switching it around can help boost your damage.
Start off with glass cannons and/or Pokemon with 1 bar charge moves, as the boss starts with 0 energy so you should be able to get at least one charge move off with your glass cannons which is quite important, whereas bringing them later on, especially against Heavy Slam might mean they get taken out before they get a charge move off, which is less likely to happen against Pokemon that are more survivable and/or have multi-bar charge moves (i.e. your Dragonites)