One aspect of this that is particularly perplexing to me is the fact that the shooter seems to brandish something with his left hand before pulling the gun out. Was it a message? Was it just a blank, or essentially blank, piece of paper to get Liz's attention so the shooter could have time to pull the gun, aim, and fire without Liz having the opportunity to become a moving target?
There are a couple of ways to read this: First, that it was a message to Liz, so that she would know the who/why behind her death. This could apply whether or not it was someone she knew or a hired killer. If someone she knew, he would have wanted her to recognize him, but wasn't sure she would without making it obvious since he was wearing a disguise. If a hired hit, for obvious reasons.
Second, and this seems quite likely to me, is that it was simply a distraction to give the shooter the best opportunity to get a good shot/shots in. The reason I lean toward this is that the moment that she looked at it was incredibly brief. It seems like it wouldn't have given her even time to process anything appearing on the paper, or register the object, whatever it was. This would seem to support a hired killer?