Ah, the LSH. Fond memories indeed.
To add a LSH feel to the universe, you should consider planet specialization -- for example, a prison planet (Takron-Galtos), and administration planet (Weber's World), and so on.
FTL is a must...there's much planet hopping going on.
Don't forget an orbitting medical facility!
Radiation accidents are common -- both for origins and for character rewrites (eg Lightning Lass to Light Lass and back again).
Roster turnover was fairly high thoughout the history of the LSH with many deaths and retirements. Some were even permanent!
The LSH universe was one where high science coexisted with high magic, so *anything* is possible!
Mix up the style/scope of the storylines -- not every event should threaten the world or universe (I think we call that "The Authority") -- throw in some mysteries, political intrigue, etc.
Borrow from classic (campy?) storylines. Have at least one member be a villian infiltrating the group; the entire team should be captured at least once and stuck in a "Super Gulag" of some kind; the team's computer servant should go crazy at least once and the team should be outlawed semi-regularly!
And finally, have situations where the most unlikely powers are the most useful (think Chemical King and Bouncing Boy).
