With no full credits at this point, the best guess at authorship has been that whatever Stan Lee didn't sign was written by Larry Lieber. In late '61, it looks as if they were indeed the only two writing for the company; that wasn't be true a couple of years earlier, where Jack Oleck, for instance, was one of the writers with a story in TOS 1 and Jack Kirby was for a short time allowed to be the writer/artist he'd been elsewhere (see Nick Caputo on Kirby's scripting his own stories in Battle).
Since by 1961 Stan and Larry's styles are very, very similar, I'd been relying on that signature; the only story signed by Stan in these six issues is "The Fourth Man" in #6. It's a small surprise, then, that he wrote some stories he didn't sign. The surprise is only a small one because they're exactly the ones you'd think he wrote: the twist-ending shorts drawn by Steve Ditko, quite a different sort of tale by this point than the monster epic leads. AA would, of course, turn into Amazing Adult Fantasy with #7—all Lee-Ditko stories of this sort and all stories, covers, and contents pages signed by Stan and Steve. In the four anthologies that outlasted AA, Stan would continue with the Ditko stories (signed and then credited, when Larry gets credit too on his stories).
Again, this doesn't stretch back years. Steve Ditko's first stories for Marvel in 1959 were not scripted by Stan Lee, who was busy enough with the Western and girls' series.
UPDATE: I'd originally listed Dick Ayers as the inker of "Sserpo," but Mark Evanier's comment sent me to look at it more closely.
|Jun/61||1||Torr||w: Larry Lieber|
|p: Jack Kirby i: Dick Ayers|
|Midnight in the Wax Museum||w: Stan Lee a: Steve Ditko|
|I Am the Fantastic Dr. Droom||w: Lieber p: Kirby i: Ditko|
|Jul/||2||I Led the Strange Search for Manoo||w: Lieber p: Kirby i: Ayers|
|TheWorld Below [DR. DROOM]||w: Lieber p: Kirby i: Ayers|
|Rocky's Last Ride||w: Lee a: Ditko|
|Aug/||3||We Were Trapped in the Twilight World||w: Lieber p: Kirby i: Ayers|
|The Teddy Bear||w: Lee a: Ditko|
|Dr. Droom vs. Zemu||w: Lieber p: Kirby i: Ayers|
|Sept/||4||I Am Robot X||w: Lieber p: Kirby i: Ayers|
|Who or What Was...the Bootblack?||w: Lee a: Ditko|
|What Lurks Within? [DR. DROOM]||w: Lieber p: Kirby i: Ayers|
|Oct/||5||The Escape of...Monsteroso||w: Lieber p: Kirby i: Ayers|
|The Watchers||w: Lieber a: Don Heck|
|The Joker||w: Lee a: Ditko|
|Nov/||6||Sserpo! The Creature Who Crushed the Earth!||w: Lieber p: Kirby i: George Klein|
|The Fourth Man||w: Lee a: Ditko|
|Dr. Droom Defies the Menace Called...Krogg||w: Lieber a: Paul Reinman|