Which one should I give for Lugia? It is a bulky fast sweeper
Let me get the mechanism of the items first. Shell bell heals the 1/8 of the damage dealt(hp reduced from the foe). Leftover on the other hand heals 1/16 of the max hp of the Pokemon holding it. A 100 level lugia can have 322 HP(0 EV and 0 IV in hp). With that amount the leftover will heal about 21 hp per turn. But the Shell bell requirs 161 damage done to a foe to heal the same. So if the lugia has more hp you have to deal more damage for the same healing of leftover. And 161+ damage is not easy to deal. So in my opinion leftover will be good for lugia. But if it is a calm mind lugia or a sweeper that can deal more than 161hp(more if it has more than 322 max hp) damage then shell bell will be better.