Actually, you may not lose your apps and data. If you install without wiping your data, then some of it may remain, though there is no guarantee it will work 
An alternative approach is to back up your LOS apps and data using SeedVault (which I believe is built-in to LOS.) and a project like Android Backup and Restore Tools
When you have installed /e/ OS, you can try restoring the apps and data
- SeedVault has been present in /e/ OS for a while, though it is not enabled in the UI. This form post describes how you can use it from the command line using
adb shell - Android Backup and Restore Tools contains scripts to restore some or all of your apps and data
Of the two, I would be inclined to try the Android Backup and Restore Tools restore first but, if you backup using both methods, you at lease have two chances that it will work 
Of course there is no guarantee that either will actually work, so you should definitely flash TWRP Recovery in place of LOS recovery, and use that to backup your existing LOS system, apps and data, so that you have a fallback if you can’t make /e/ work. For peace of mind, try restoring your TWRP bacjup, before you set about doing anything else.
If you choose this approach, it’s not something that can be done in a few minutes. you would need to set aside a couple of days to work on it, and you will be without access to a working phone for a good part of that time.
Good luck!