if it's your first character and questing for the legendary weapon, hunt it while also hunting the other items. Example, while you are hunting 400 feathers or whatever, once in a while, visit abyss_02. Then if you come by lost dragon but was not lucky enough to get the hero's remains or was killed by other players, then try your luck again after 20 minutes and hunt those other requirements. There will come a time that you'll be able to solo the Lost Dragon and get its loot. Not all the time that someone is hunting it. This way, your time is spent well and you'll finish the quest faster.
if you're just casually hunting the remains to sell it later for zeny or toks. then, i suggest you follow what @Rayray said. Or create a High Wiz/Baby Wiz. Why? Because you could also use it for farming services too or zeny grinding. Also JT kills the sh*t out of Lost Dragon. @mi it and you'll know the benefits behind JT and High Wiz/Baby Wiz.