Worth the candy and dust?
Answers
What's his IV's?
It looks pretty low IV (sub-2000 CP), and Lugia isn't particularly useful. It's a tanky, potion efficient generalist attacker, but it's slow due to it's low atk.
I would say no - there are much better uses of dust (dust is now the limiting factor for most players, and I really regret powering up some mons, since now I have candies and good IV things for lots of mons that I need, but can't power them up). I powered up my 98% one, though I sort of regret it now - I should have prioritized the dust use differently.
I'm more than pleased with its IVs: 13a/13d/15s--I'm not as picky as some on the internet, the world's not perfect and neither are my pokemon. If you find yourself taking down gyms more than constantly building supreme raid boss counters, Lugia is a potion efficient option in that capacity. As many have noted it can also be a tank option in certain raids.
My deductions have it as 12a/10d/11s. I wouldn't put it as a priority, but at some point stardust will be easier to obtain and we'll have a better idea where the game is headed. I just like to put a very little bit of dust into my main legendary birds, just to not have it at level 20. 2500x2stardust isn't that big a deal either way, but it makes me feel better
Why didn't you tick the highest stats (Attack/Defend/Stamina) from Appraisal? This helps narrow down the IV range.
[2nd Edit] I can also see one result is with 14 Stamina and the other is with 15. That means you also didn't choose the range of your Lugia's best stats from the dropdown above the CALCULATE button? Fill every option with what you know from your team leader's appraisal.
Also recharge your phone. You're killing it at 10% battery left. Try to keep your phone battery between 40-80% and it'll last much longer this way.
Also, turn off your phone, PC/laptop and go to bed right after seeing my post. It's freaking 2:25 am! :(