You have a program, Carbon Copy Cloner (CCC), that is similar to what I have, SuperDuper!. It might be best if you make a bootable backup/clone with CCC. But, as you say, it is preferable to have a "clean" system.
There are some cleanup things you can do which are not "painful". First, if you have either Disk Warrior or TechTool Pro, they could be real helpful in performing disk maintenance/repairs. But, if you don't, then you'll need to rely on Disk Utility. So, here is what you should try first.
1. Get rid of any stuff you definitely do not need.
2. Assuming that there is a Recovery Partition on your machine (created when Lion was installed), you can boot to that partition by pressing the Command and R keys. This link discusses this partition, and what you can do with it:
https://support.apple.com/en-us/HT201314
Notice that it says "Verify and repair connected drives using Disk Utility". When you do that, do a Verify and Repair Disk at the
Volume (top) level, then do a 1)Verify and Repair Permissions at the
Partition Level, and 2) a Verify and Repair Disk at that same
Partition Level.
3. After completing #2, reboot your machine. Then, download the excellent free program Onyx. This venerable gem has been around for quite some time, has had numerous positive reviews, and works as advertised. I can tell you from personal experience that is all accurate, as I have been using it for quite some time as part of my weekly disk maintenance/repair/backup processing. You can get it from here:
http://www.macupdate.com/app/mac/11582/onyx
Note that you want version 2.4.8, for Lion. It is listed under the "Related Links" title on that link. (If you do eventually install Yosemite, make sure to go back to that link and download Version 2.9.6).
When you run Onyx, I recommend doing all the Maintenance and Cleanup tasks. Note that one of the Maintenance Tasks is "Repair Permissions". Even though you already did this with Disk Utility, do it again, as Onyx will repair permissions for non-Apple applications also (Disk Utility does not).
4. After doing that, re-boot your machine, and see how it responds. A couple of other things you can do are 1) permanently remove all Deleted EMails from your machine, and 2) defragment and optimize your internal drive. Regarding #1, not sure which EMail program you use, but I use Outlook. In order to permanently get rid of deleted EMails, it is necessary to rebuild Outlook's database. There is a way to do that (and I do it every week as the first step in my weekly disk maintenance/repair/backup processing). As for #2, if you had TechTool Pro, then it includes such functions. I do not know of a good freeware program which can perform those tasks. Maybe someone else can point you in that direction.
In any event, if the machine responds better after #3 (and when you boot it up), I would think that would be the time to make a CCC backup/clone of your system.
If the Recovery Partition is not there, there are a couple of ways to re-create it. But, you'll need to have the file entitled "Install OS X Lion" (I think that is what it is called; for Mavericks, it is called "Install OS X Mavericks", and for Yosemite, "Install OS X Yosemite"). Also, make sure you have a copy of that file somewhere else. (By the way, that is one advantage of CCC versus SuperDuper!: it can make a backup/clone of that Recovery Partition. For me, though, that is not an issue, as 1) I rely on TechTool Pro (and sometimes Disk Warrior) for disk maintenance/repairs, and 2) I can easily re-create that Recovery Partition after a SuperDuper! restore (I did just that the other day on my MacBook Air)).
As for upgrading to Yosemite and running with only 4 gig of Ram, that will depend on the type of processing you do. I have the latest version of Yosemite (OS 10.10.3) on both of my machines (a late 2012 Mac Mini, and a mid 2013 13" MacBook Air), each with 4 gig of Ram, and Office 2011 (Outlook, Word, and Excel) works fine (along with other apps I use: Chrome, Firefox, VLC, TechTool Pro, Onyx, SuperDuper!, Quicken 2007, etc.).
