First of all, the Lakers are not going to rebuild through the draft!
They still eat up payroll. Asik, Horford, and Lopez will all make big money.
Think about Pau Gasol with the Grizzlies. For years, they remained in mediocrity because they were too good to get high draft picks, but not good enough to compete. That's what will happen if you get Horford or Lopez and try to build around them. They won't attract FAs either. Being in LA won't attract FAs alone. Otherwise, Dwight would definitely stay anyway.
Being devoid of any talent is better than being a mediocre team. That's how you get difference makers like the Cavs did with Kyrie Irving. The extra cap space of the Lakers could be used to get more draft picks by taking in bad contracts later on.
Secondly, why would we be mediocre if we did one of these deals?
Horford is a two time all-star at only 26, Lopez (24) have been the best C in the league this season and Asik (26) is a defensive specialist, who along with the other prospects from Houston would complement our current team. Except for Korver, the best 3pt shooter in the league, the rest of the guys i mentioned are all on minimum deals and all are playing extremely well.
We would have a very solid and even relatively cheap team going into the 2014 free agency and depending on how much Kobe wants in his next deal we should be able to sign either 1 max or two very solid players.