Zoners should normally allow you to dock on FP11 as long as you don't cause trouble.
Might be a bit strange seeing a LSF vessel around there and many will ask what you are doing there, though I see no reason why they would deny you permission to dock.
Though if you are planning to base your operations of of FP11, I'm not sure how much they are going to like it. Depends on your behaviour I guess...
The problem is, almost everything a LSF vessel could do out there WILL cause trouble. And some Order pilots won't be happy seeing you flying around right near their backdoor. iRP you might want to stay rather quiet, at least when you think there may be Order ships around.
And about the "hey, just lulwut around in the omicrons" players - yep, you are the ones he's talking about when referring to bad reputation.