Basically you get the concept, thou with how you described it that's for a purist MMR system. You'd see their MMR be lower. Its a bit more complex with League. In this case Riots system gives you a title.
I know 2 ways to make a title represent skill.
1 is player population. Your Titles are given off percentile markers. This system kind of sucks... because RNG of who is online and RNG of active players shifts constantly so the values are not inherently great for accuracy. It also does not have any overlap with MMR, which MM uses. Overall... its the weaker of the two ways I know if you care about trying to make your title represent skill. (title is division and Rank. s4 is a title. GM is a title. etc.) So I doubt riot uses it, as a dev I would never do this. Some do, they want to encourage players to constantly play at all times as much as possible. Take a look at how challenger functions to get a feel what its like when only X # players can have a rating. Inactivity boots you out.
So I assume that riot used instead this method to have titles = skill. The title represents an expected range of MMR at low uncertainty. For example lets say 1200 to 1250 is what's used for Silver 2. Any player with a rating of 1232 who hits lower uncertainty (enough games played that you feel your system has filtered out some luck and RNG of teammates/enemies. My rule of thumb is the "veterans" Badge that's 100 games in the Tier.) Would be sitting at a Title of Silver 3-Silver 1. This is because individuals don't always have the same Range, some are more feast or famine some are more consistent. The wider your best and worse performances the wider you see folks place off a recent trend of games.
So your LP slant then would be generated off the gap of your MMR, Your title, and the MMR value of the game MM created. This value would be consistent for any account thou its unlikely to be all that common as variables tend to.... well... experience Variance. Go figure.
The MMR and Elo systems work of a probability theory and distribution model. If your curious I can provide some links for self study. If your not interested in learning the math but want to achieve a "working knowledge" I am happy to take a stab at any question and try to turn the math formulas into englsih for folks but you should take it with a grain of salt cuz there's a risk that 1) I don't account for what riot did properly. 2) Just have a flaw in my understanding I have not caught.
For the most part, if you understand Why Rn= Ro+K(W-We) You have a good starting point to understand MMR/Elo systems and the various derivatives. When you get the logic of why, you have a spot to start looking for issues implemented by devs.