I plan to boil a fresh lobster.
Serving it only with melted butter and lemon seems like not enough.
What would be a good side dish for it?
I would suggest anything that you can grab easily and is not difficult to eat. You are going to have to get dirty cracking the lobster, so why not get some corn kernels on your face? Growing up in New England our lobster dinner included sweet corn on the cob and cornbread. (The butter can be used on all of it!)
Also, if you want some greens, maybe some steamed broccoli?
In terms of flavors, are you going to just do a salted water boil or maybe add some old bay? you can even add bay leaves to the water. If you are adding flavors to the lobster while boiling, think of how those would go with the sides.
Lobster is really popular in North Western France. I've seen it served there with crawfish cocktails and oysters; something like this.
You can also just keep it down to earth and simple. In New England I used to eat lobster with french fries. Not quite worthy of Brittany, but yummy all the same.