I think it's really important (in the minor context of this thread!) to note that money doesn't really change your class: you aren't catapulted up to upper middle class by winning the lottery. You don't become lower middle class by not having much money if you were previously middle class - those parts are changed partly by money but significantly by cultural capital - pastimes, hobbies, social circles.
It is possible to change class but it generally happens a generation later usually I think?
My parents didn't have much money when we young, but we have land, and education was highly valued. Their parents both worked in traditional professions (actuary, dentist). Their friends were generally in professional jobs - software engineers, lawyers, accountants, structural surveys, teachers. Their hobbies are middle class: art (viewing and doing), classical and modern music, gardens, cultural heritage stuff). They are very middle class in spite of the lack of cash, and my siblings and I will be higher earners than them because of their focus on our education. (While likely remaining middle middle class.)
Then there are people like my friend: her dad grew up in a solidly working class household. He went to grammar school and then a polytechnic and became a salesman and was incredibly well paid: far better than my parents - but they are realistically still lower middle class. On the other hand their children are solidly middle middle class.
Then you have the upper middle class: probably public school, probably a second home somewhere smart, most likely a highly paid professional and almost certainly middle class for several generations previously on at least one side of the family.
I think my feeling about this is that you can change class but only one "rung" per generation.
So working class growing up, make plenty of money and take a middle class job and you'll probably transition to lower middle class. Your children might be lower middle class too, or they might hop up a rung into middle middle class, depending on what happens with their education etc.