It's actually not as bad a trade as people are suggesting.
I like what I see of Brown, he has some undeniable upside. However it's still too early to predict how high that ceiling actually is - Jimmy Butler, Rudy Gay or Jeff Green? Too hard to tell until at least a month after the All Star break, since that's usually about the time when rookies start to really show their potential.
On the other hand Covington is a really solid wing who can stretch the floor, he'd make a nice backup SF and would probably fit the team well.
Noel is a very young and extremely athletic 7 footer who can rebound the ball, has elite defensive potential, and actually probably has more offensive potential then most give him credit for. Not saying he'll ever be a good scorer, but he's got the potential to be able to at least be productive on that end of the floor. The injury history is a bit of a worry, but he seems to have maintained a good motor and work ethic despite playing on the 76ers, and that says a lot about his intangibles - in the right team with the right culture and tutelage he could be something really special down the line.
The Lakers pick is tough to call. I feel they are overachieving right now and I do believe they will drop off and become a bottom 10 year, and as such that pick probably will fall into the top 10. The way the Nets are playing, there's some chance that pick might not be far off the Brooklyn one. Having two top 10 picks in next year's draft is a pretty nice prospect.
Losing Brown would hurt, but we'd have Gerald Green, Covington and Smart who can all fill in minutes at that position, so we could survive it.
When I first read the OP my response was an emphatic "no!", but the more I stop and think about it the more I lean towards yes. It's a pretty good deal and probably makes sense for both teams.
For us:
Noel is exactly the type of big we need alongside Horford and offers us extra rebounding and rim protection that we desperately need, while Covington/Green combined give us plenty of depth at the wing positions and the Lakers pick gives us the potential for two top 10 picks in the 2017 draft.
For Philly:
They get an athletic, high upside swingman who can score at the basket or from the perimeter and who has the potential to be a versatile two-way threat. He'd be a perfect fit alongside Embiid and Simmons with those three guys forming the perfect "big three" to build around. If they then move Okafor for a decent young PG they are in business.