Am I ready for Machamp solo?

Is it even possible to have a Lugia with 8 defense?

Looks like a solid team to me. Just to be on the safe side, I would probably power up both Lugia a bit more so that they can survive a bit longer, if it ever comes down to that. As for your 6th candidate, definitely the lvl 23 Exeggutor, ES with stab will be optimal against Machamp, along with SB as a powerful charge move. Once you've done these, you'll be more than ready to go!

At around level 34 you can do Machamp with 2 strong psychics (34), 1 30ish psychic and 2 neutral high DPSers(30).

If you throw out the Lugias which are too low leveled and take the Exegguttor to 32 you are more than well equipped.

For comparison, I managed to solo a weather-boosted Machamp with BP/CC using this team:

1. L30 12A/15D/14S Espeon with Conf/FS
2. L30 15A/15D/14S Alakazam with Conf/FS
3. L30 13A/15D/15S Alakazam with PC/FS
4. L30 13A/14D/13S Exeggutor with Conf/Psyc
5. L30 15A/13D/15S Exeggutor with Conf/Solar
6. L30 14A/14D/11S Dragonite with DT/Hur

You are ready, altough i will ditch the Lugias and powered up that exeggutor to lv 30, and bring in that gengar

This is what i used when i feel like it to play around a little, no legendaries, no dragonite
But yes, your team is good enough, level 30 can win against Machamp (not quite easy though)

https://m.youtube.com/watch?t=9s&v=7Je-BlQcH-E

What level is you Alakazam with Shadow Ball and does it have Confusion? At level 30 a C/SB Zam has a 160ish time to clear machamp so it might be worth a look.

Dragonite is a more useful tank (not better per se than lugia vs Machamp) but has so many other uses outside of Machamp solos. I’d recommend powering up a dragonite with Hurricane or Outrage as long as it has a dragon fast move.

So in summary if I were you the cheapest way to get ready might be to run with:
Espeon
Espeon
C/FS Zam
C/SB Zam—if this isn’t Lv 30+ go eggy/lugia
H/SB gengar (vs fighting movesets)
Powered up dragon

If the SB Zam isn’t high level then power up either of your eggys (E/SB or E/P) or the lugia (FS since you already started there). Another option if you happen to have one is Gardevoir (but I realize those are harder to come by).

TL;DR
My lineup using your Pokemon would be:
Espeon x2
Alakazam
Exeggutor x2 (powered to level 30)
Lugia (powered to at least level 27.5)

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The Lugias will need powering up if you want to bring them to the raid and have them be useful. You want to at least hit the 12 damage breakpoint on Extrasensory which is level 27.5 for either of them.

Sky Attack is the better move but Future Sight is very close, so it just comes down to whether you want to spend extra candies and dust. The difference in IVs is negligible.

The level 33 Espeon can be levelled up one more time if you wish, as the next Confusion breakpoint is at level 33.5, though Confusion being a slow and high damage move benefits less from +1 damage per move usage compared to other moves.

The Alakazam is fine to use as is, but is also close to the next damage breakpoint which is at level 34 for both Confusion and Psycho Cut.

If you are going to level it up to 34, I would suggest Fast TMing as well if you've got plenty of fast TMs, not only will you benefit more from hitting the breakpoint because you can get more attacks off in total and therefore more damage, your chance of winning is less influenced by bad luck - i.e. missed dodges.

With 3 high level glass cannons you should have more than enough DPS and the only issue would be if they fainted earlier than expected because Confusion was too slow and caused you to miss a dodge.

Take the Exeggutor to level 30, as Extrasensory goes up in damage if you've got 13 or higher attack IV. Solar Beam is fine even though it's not super effective. There is no need to take it up any further as there is a negligible difference, all you are getting from taking it to level 32 or 33 is a few extra points of HP and few points of damage on your charge move.

The Gengar you can bring if you have nothing else and don't want to power up better counters. Hex + Shadow Ball actually has an expected time above 180s but is still fine because the Espeons and Alakazam will make up for lost time.

The problem is that it's only really useful against fighting movesets due to it's triple resistance but with your lineup you shouldn't have an issue with fighting movesets anyway.

If you happen to already own a powered up Dragonite with Dragon Tail + either Hurricane or Outrage I'd use it instead of the Gengar, because even against double fighting Machamps, Dragonite performs better in both total damage and DPS, but is also much more survivable against Heavy Slam.

I'd only use 1 Lugia and in the 6 hole - to hold on. The race is against the clock. Get a higher attack stat for the 4th & 5th spots.