It makes perfect sense to believe it signifies “a lot of affection.”
When it comes to text message terminology, there should be a guide sheet for parents. “lol” seems to have been used at the worst possible time by this mother. Fortunately, David was able to correct his mother before she spread the word to anybody else!
Even if you want to, you can’t truly hold it against her. So, if it implies “a lot of love,” that makes sense. We just hope she didn’t insult any of the folks she phoned back!