For the problem of not having the same graphics of the game and the recording, there are different situations
1. The graphic of the recording is way far lower or lower than the game all the time. Mostly it is because of the setting of graphics of the recording, changing the graphics of the recording from the app that record the game video might help you.
2. The graphic of the recording is way far lower or lower than the game sometimes. Maybe the problem is the most normal situation, lagging. It might also because too many apps was opened and operating at that time, causing the GPU or CPU have exceeded workload. The problem can come up because of the limitation of GTA5.
For situation 1, just change the setting at your own choice. (Some video recording apps might require subscription to have high graphics on the video)
For situation 2, the following instructions might be able to help you:
1 Closing apps that are not needed at that time.
2 this video might help: https://www.youtube.com/watch?v=PmrWXnmOpcM Start doing the instruction given at 1:39(As The viewers are the most important at all times, updating driver is the best way to fix lag)
3 If that fix still unable to help or can't make the fps to 50-60 (It's kinda high fps for lspdfr already), you might have to disable V-sync(Hope you don't need to, cause it might lower the graphics performance or whatever it calls, doesn't matter)
4 If V-sync still doesn't help, think about reducing the traffic and peds by installing a gameconfig with x0.5traffic and peds. https://www.gta5-mods.com/misc/gta-5-gameconfig-300-cars (Remember to install the heap adjuster as it is the requirements).
5 If those 4 on top still don't do any help (Hope it does help), reduce the amount of plugins (Delete the plugin that is outdated or haven't been update for months and plugins it isn't useful to you.) You can also try to install plugins that you will use in that video only. (I know it's annoying and making you crazy, but it could be effective)
6. Reinstall GTA5 (Not Verify). This is the most effective way to fix the lag, but also the way that is making people crazy(At least I do)
7. Lower the graphics, like reducing the special effects, blah blah… (And yes, it might lower some viewers interest, some people do, not me)
8. Only do this if you have tried all the instructions on top, and it doesn't increase the fps to the level that you wanted (I suggest the fps levels to be wanted is 50-60, as recording videos also lower the fps performance), upgrade your computer.