Well,
FYI,
OS X 10.7 was not a very good OS X version, at all.
Generally, it WAS slow and buggy and never got much better after it went to 10.7.5.
OS X 10.7-10.7.5 were still kinda a mess and, definitely, felt like an unfinished OS, IMO.
I dumped it after 10.7.2 and waited it out until the next major OS X versions.
I waited until OS X 10.9 Mavericks came out and later, to be able continue using some of my older software that wasn't as stable working on OS X 10.9.5 Mavericks, I went and reverted back and paid to download and install OS X10.8.5 Mountain Lion.
I think I am one of the few OS X users that really like both Mavericks and Mountain Lion.
Both run great on my older 27 inch screen,2009 iMac. For some reason, though OS X 10.9 takes longer for my Mac to boot, but once booted, it seems to run fine with nary an issue
I have found OS X 10.8 Mountain Lion really was what 10.7 Lion should have been from the getgo, but it still has some PITA issues right up to 10.8.5 that I have to work around, but I find it is very stable on my Mac and all of my older problem software runs a lot better on 10.8.5.
I have OS X 10.11.5 El Capitán, also.
I find it does run faster on my older iMac, as well, but I don't like the flat "PlaySkool" looking icons and the general gray, stark looking UI and windows.
Plus, much of my software won't run on it and the features I wanted to be able to use and take advantage of to use with my newer iPads, are not available to my year and model iMac.
So, El Capitán is of little use to me.
I downloaded and installed it mainly for use with any iDevices that may need future iTunes versions to sync to it and for those times when I might need it.
I do not know if I will bother with macOS Sierra or not. There will, in all likelihood, not be ANY specialised features for my 2009 iMac to take advantage of.
Plus, I don't see any other compelling base features to bother with OS X Sierra, either.
OS X 10.8 and 10.9 will be my go to OS X versions for some time.
Your iMac year and model has access to all of the new and cool features of El Capitán, so I am a little jealous.
As Far as your Time Machine backup goes, Time Machine, if memory serves, only backs up files, data and applications. Nothing strictly to do with the OS X system.
So, if find any issues/deal breakers with OS X El Cap, you have no way to revert to your previous OS X version.
You will be faced with using OS X Recovery Mode to do a complete reinstall of OS X 10.7 Lion (or redownload it under your purchased history within the Mac App Store) and you will have completely reinstall all of your installed third party software from scratch and will have see if your Time Machine backup data will be able to brought back into 10.7 Lion.
That is why I stressed a new hard drive and cloned, bootable previous system backup.
Too late for that now.