How about a sign that says "Please take your dog to someone else's garden."? Seriously, as a dog owner, I can tell you that if I didn't stop him, my dog would mark everyone's gardens -- it's like a magnetic attraction. If you can plant a small evergreen shrub or two where the dogs are most likely to pee, that may keep them from the lavender. The shrub will survive the urination, and look none the worse for wear.

I personally am not offended by neighbors who say "I'd really prefer not to have dogs in my yard." At least the neighbors who say it nicely (but that's another long story...)

There's a new annual out that is supposed to discourage dogs and cats from visiting, called Scardey-Cat Plant, Coleus canina. I have no idea if it actually works, but it certainly smells like it would: very pungent indeed. According to this site it has been very popular in Europe. I saw them recently at my Home Depot.

Here is a link that might be useful: Scardey-Cat Plant

How about something thorney? I'm sure a pet of any kind would prefer not to get his specials pricked by a thorn.LOL
You could try some Prickley Pear Catus. Sounds like the spot would be perfect for growing Catus.The hotter the location the better. Once their established, They are virtually maintenance free, And a conversation piece. They are low growing and very pretty in bloom.I had some in a large wooden barrel and they wintered over just fine.I don't see why they wouldn't do the same in your flower bed.It couldn't hurt to try.

(Well maybe a little)LOL

The prickly pear cactus is an intriguing idea, but I think they're too big for this yard. (We're on the corner of the alleyway, and the yard itself is 26' wide by only 9-10' deep.)

I'm thinking I might try snow-in-summer in the corners of the quarter circles; I like the way it's established itself in the second year in other places. It seems to stabilize some little slopes and smother the competition.) Then put the lavender behind them.

the idea of something thorny by the walkway to deter the dogs is a good one... you could use some prickly shrubs like cotoneaster or barberry....if you have enough room. they would be more attractive along a walkway than prick;y pear cactus (though that is what they used in the deserts and prairies to make natural fences to keep livestock from straying) .... but the problem with that is that if you dont have enough room when you, your family and visitors have to walk past it and theres not enough room then you dont want to risk someone getting scratched by something thorny by the walkway. id be pissed if i ran my stockings as i visited a friend....
i actually vote for the go away dog sign lol if i was a dog owner out walking my dog and saw your sign i would be damn sure NOT to let him do his business in your yard.

Sue
"The one thing all gardeners share in common is a belief in tomorrow"

Have you researched herbs? Some are fairly attractive and with their strange odors, there might be something useful in that group...

I've seen a little 'sign' in several yards lately. It's a white wooden cutout outline of a dog squatting (on a stake, so you can stick it wherever,) painted with a face and some features so you can tell it's a dog and it has black letters: NO! It's about 8-10" tall and it makes ppl giggle. I can't speak for its' effectiveness... What sign can one try for keeping out cats? Hahaha!