Lugia moves

ES/FS only use is soloing Machamp.
DT/SA is only usable for Mewto. After Mewto it will be a tank like Snorlax and Ho-oh will be released one day with SA too and will be a much better generalist. It's a tricky choice here. I have a 14/14/14 Lugia with DT/FS and think about how to use it too.

CTM first to see if u get SA. Keep DT if thats the case. If its FS then FTM for E.

My best Lugia had the same moveset and I did as suggested above. Used Charge TM (weeks ago) and it went to DT/SA. I have not touched it since. Good for MewTwo, for the moment.

If the only thing that worries you is Mewtwo then honestly keep it as DT/HP until after Mewtwo goes (it too will probably be temporary like the birds) then change it afterwards.

For reference Pokebattler reckons that against Confusion/Focus Blast Mewtwo raid that 6 x level 30 DT/HP Lugia will take 23.8% of Mewtwo's health whereas 6 x level 30 DT/HP will take 21.6% of Mewtwo's health. So on average for one Lugia the difference between the output by DT/SA Lugia and DT/HP Lugia is 0.37% of Mewtwo's HP. Not worth it to change moves solely for Mewtwo in this case.

Personally I changed my Hydro Pump Lugia to Future Sight to serve the dual roll of helping to solo Machamps AND make soloing Focus Blast Gengar a piece of cake also.