Personally, I do think the league has rigged the lottery at times. The most suspicious instances are when a team with nowhere near the best odds ends up getting the top pick when they just so happen to desperately need it, so to me, Boston getting the first pick isn't suspicious at all because it was the favorite to do so.
On the other hand, the Cavs winning it in 2014 despite having a 1.7 % chance to do so? Highly suspicious, IMO.
While Boston-LA is obviously the best rivalry the NBA has ever had, I don't think the league has had any incentive to help the Celtics in a long time. First, even when we aren't winning, we still draw better than a lot of teams that are winning (and astronomically better than other losing teams), so there's very little financial incentive to make sure the Celtics are good. The vast majority of teams in the NBA play in front of empty arenas when they aren't any good, so those are the teams the league has an interest in helping.
Second, all the league cares about is maximizing its profits, as it's a business. The Celtics have a large fan base, but don't have anywhere near the "cool" perception with casual Sportscenter fans on a national scale that draws in new fans and bandwagon fans. Even if we have an entire roster of black players, we'll always have the reputation as being the team for white people, which often translates to "not cool" in today's basketball landscape. On the other hand, even if the Lakers have an entire roster of white players, they'd still have a much "cooler" perception than the Celtics. For whatever reason, the Celtics really struggle when it comes to national popularity among fans 35 and under (obviously excluding the New England area).
On the other hand, teams where the fan base only shows up when they're winning need much more help from the league. Back to the Cavs for a second, the league didn't know in May of 2014 that LeBron was going to return. Did you ever watch a Cavs home game while LeBron was in Miami? It was a graveyard in there, and would've continued to be so if the league hadn't stepped in to give them a boost.
I don't think the league rigs the lottery every year, but certainly has in the past and likely will in select instances in the future.