So I’m downgrading the OS from Mojave to back to Lion..backed up hd with TimeMachine. I will erase the drive and install the older OS. My question is will I be able to restore my applications from my TM backup?
I am afraid it may depend on if you use an external hard drive for Time Machine backup or not. Since most methods to downgrade macOS are related to erase the internal hard drive which contains your original macOS. So it would be great if you have backed up files with an external hard drive because you can Restore your Mac from a backup.
Another suggestion is that, if your Mac was installed with Lion when you bought it, you can reinstall to Lion by rebooting and holding Shift-Option-⌘-R As this support post said Reinstall the macOS that came with your Mac,without easing the disk, unless you want to to. Like it said: You probably don't need to erase, unless you're selling, trading in, or giving away your Mac, or you have an issue that requires you to erase.
You will be able to restore everything from the backup which was done on the same or an older version of macOS Lion (10.7.5 was the latest, so if you just downloaded it from the App Store, you will probably have this one).
From later backups you have to copy/paste everything manually.
Also for Apple apps like Safari, iTunes, etc. only the latest version that was provided for the OS version your are about to install will be available, eventhough you haven't updated it to that version at the time of the backup.