As far as i'm aware there are only two real criteria for it:
One, the fence must be suitable for the region you're in. Glade only works for Lavender Beds, but i think you got that part.
Second, as long as you remove the current fence (thus reset it to the default one) first, you can add in something else as far as i'm aware. Replacing isnt an option because the current wall would be void and gets deleted opposed to being returned to your inventory.
And that's really all there's to it.
Do take note that there is a diffirence between being allowed to place furnitures and being allowed to modify the very structure of the house through remoddeling. I know i myself am allowed to do and edit everything up to remodelling the house, just not touch the very house itself. That is something that is only set to the FC leader by default and i am not aware if any such options can be made available to officers. Probably though.
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[XI] Surivere of Valefor
[XIV] Sir Surian Bedivere of Behemoth
http://na.finalfantasyxiv.com/lodestone/character/2401553/