Lakers have the same roster, so their chance will still be the same last season. Even if Davis will be healthy but if Westbrook will remain struggling, that will not help the Lakers as Westbrook is surely a starter again. Melo getting a ring, that sounds nice, maybe he can retire after that.
We can't compare the Lakers and the Warriors, both could have the same chances last year, specially Lakers wherein there is a high expectations on them. While the Warriors were not among the favorites by suddenly even without Thompson in the first half of the season, they manage to stop on the top 3 in the West. So let's see if Melo can even land to a decent team this season, him, Dwight and others are still free without any offers.
I'm sure these two will get an offer because they will easily fit into the budget of any team due to their low amount of contract. If Melo will and with the Warriors, no doubt he will be a big help as it has not happen the Warriors acquired a player that they did not utilize well.