I was thinking about your blanket border and I don't know if I have a satisfactory answer for you or not - to find a knit in the round lace pattern, I googled circular shawl patterns and found one with a lacy border like this one
. It is knit in the round and I do not see a reason why you couldn't add it.
The only problem I see is the fact that you want to add something round to something presumable square or rectangular. And, I am afraid that it won't lay flat when you are done.
I think the easier thing would be to add each side one at a time and then just seam up the little section where they two new sides meet. I think most people crochet borders on to blankets so they don't have this issue! :-) Good luck!!