I would agree about confirming identity, except that it doesn't appear that Liz had a chance to say anything, or nod...she seems to be just listening.I speculate it is motive related, but could fit more than one narrative.
If it was personal and they knew Liz well "He/that was MINE!" "You remember (insert action)?".
If this was a hired hit, they could be confirming Liz's identity. But....I would like to mention there is not shortage of mistaken identities murdered on a hit. See Daniel Ott (happened to be two in that small town), Doug Johntson who was driving a nearly identical car and lived on the same street as the intended target (See Chuck Morgan case) Angela Hammond being abducted after being confused with a different Angela who looked a lot like her, and the high likelihood that 2 Mary Morris's were killed in the same town under mistaken identity during a hit.
I'm trying to imagine how it would work for the killer to have no interaction. She said good morning, they probably wanted to get closer up to her before shooting, so may have just blabbed some small talk to justify coming right up to her, without having even looked at any of her stuff.
I think it's quite possible the shooter was just spouting nonsense, stalling for a few moments, in order to get into position, gather his/her focus and take Liz completely by surprise.
JMO