It would help if you had a lotto pick that sat out a year (or more). David Robinson, Danny Ferry, Greg Oden, Ricky Rubio, Blake Griffin, Jonas Valanciunas, Nerlens Noel, Joel Embiid, and Dario Saric come to mind.
Everybody but Ferry and Noel played their rookie year with another lotto pick, and Noel could have played with 2 others had Philly not drafted 2 more guys in the lotto who wouldn't play that year.
LAC came close in '10 with Griffin (#1 prior year), Aminu (#8), and Beldsoe (#18).
Not all lotto, but Portland had 4 first round rookies playing in '09 (#1 prior year, #11, #24, #25).
There's only been 32 lotto drafts, around 400 lotto picks, and maybe only 9-10 of them who had to sit out their rookie year, and Philly drafted 3 of them in 2 years? Guess it shouldn't be surprising that Philly is the first. They definitely have the formula down for it.
I also thought maybe Chicago post-Jordan, as I remember they had several years with multiple picks. It looks like they didn't do it, but man did they have a string of lotto picks (and they were only terrible half the time).
'99: 1 and 16 (Elton Brand and Ron Artest)
'00: 4 and 7 (Marcus Fizer and Chris Mihm. Mihm traded for Jamal Crawford)
'01: 2 and 4 (Tyson Chandler and Eddy Curry)
'02: 2 (Jay Williams)
'03: 7 (Kirk Hinrich)
'04: 3 and 7 (Ben Gordan and Luol Deng)
'06: 2 (Lamarcus Aldridge traded for Tyrus Thomas)
'07: 9 (Joakim Noah)
'08: 1 (Derrick Rose)