Is there any way the hair in my eyebrow can grow back after a direct unilateral browlift?

this is an interesting question and given it is so early, i'd advise you to give it some time. The odds are, the hair that was removed will not grow back, but you may be surprised once your brow "thickens" up a bit. I wish I had a better answer, but I think waiting is the key. 

With the direct browlift, the upper row of brow hair may either trimmed, or fall out with the procedure.  We try to bevel the incision so that the hair will then grow through the scar as it is healing.  So give it some time and hopefully the hair will return.    

Since you had your unilateral direct browlift only a week ago, I would say that your brow hair may grow back with more time.  I would wait at least 3-4 months to see if you get any improvement.  If there is no improvement, hair transplants are an option or you could try using Latisse on your brows to see if that helps.   

One week after a unilateral brow lift surgery, you should be patient and wait to see if the hair will regrow. Quite often after surgery, there is a shock to the local hair and they fall out. After several months the hair returns.

If the incision was made correctly then your hair should grow back over the next 3  - 6  months.  Give is more time. 

Since it has been such a short time since your surgery your hair loss may not be permanent. If this is the case you will see the hair follicles start to appear over the next few months. If the hair follicles were completely removed then specialized hair transplant techniques will give you the best long term results.