My FIL used to do this. He wasn't (and isn't) and evil or horrible man, he just genuinely doesn't know how to react to children and has never grown out of the notion that teasing is 'fun'. FWIW I will outline my thoughts and actions that I undertook in the hopes that your friend finds them useful. DDs are now adolescent and do have a healthy, but not close, relationship
with their Grandfather.
1. I don't like the 'leave her to have a tantrum' idea. Firstly, it should never get to tantrum stage, secondly it is not supporting DD when she has been emotionally hurt by someone she trusts and thirdly (and least importantly), it's not teaching the daughter about appropriate behaviour which at 4 she is old enough to *start* learning.
2. We didn't want to go with a nuclear option so we went with teaching DDs that "Grandfather is a tricker". As soon as he started on one of his idiotic stories we'd casually say with a smile "Remember, sweetie, you can't believe that because GF is a tricker." Grandfather heard "Because he's such a jolly joker and we'll all play along" and so a fight was avoided, whereas the message DDs got was "Don't believe a word he says". Very quickly DDs didn't need prompting, they'd just say "You're being a tricker, GF" as soon as he started. He gave up because it wasn't fun anymore. It's important to note that our attitude was key. We set the tone for DD's reaction by our attitude of "Yeah, whatever, not worth getting worked up about, it's just GF being silly. Ho hum."
3. There was a less immediate and very real consequence to his behaviour. DDs adore MIL. They are fond of FIL but there is just not ever going to be that level of closeness that they have with their other grandparents.
This same pattern has happened with every single one of his grandchildren. By the time the third one rolled around their siblings and cousins would just say "Oh, don't listen to GF, he's just being a tricker
" and the parents had to take very little action.