Hi, LGM!
Nothing at all mysterious about cleaning a lever-action rifle.
You need cleaning tools, of course: rod, bore brush, slot or jag tip, swabs, solvent, and oil.
If you don't disassemble your lever action rifle, you must clean from the muzzle end using a rod. If using a pull-through or flexible "rod", you can clean from the breech. Just be careful not to rub on the muzzle or lands when working that rod. Many rifles have been prematurely worn-out from improper cleaning technique.
1. Standard bore cleaning procedure: swab out with solvent soaked patch on jag, follow with bronze bore brush if needed (if shooting lead bullets, you will need it), followed by solvent-soaked swabs, dry swabs, and protective oil. make sure all copper or lead fouling and powder residue is removed.
2. Standard action cleaning procedure: use thin tooth brush or small paint brush with cut-down bristles to remove most powder fouling, dirt, unburned powder, etc. from bolt face, action rails, crevices, etc. Follow with solvent and rag to remove residue, dry, and oil. Add a drop of lube oil to all bearing surfaces, work the action a few times, and wipe off excess.
3. Wipe down exterior with lightly oiled rag.
4. Infrequent detailed stripping for cleaning and oiling EVERYTHING, inside and out, including magazine tube, spring, and follower. I do this maybe once a year, after hunting seaon, and before long-term storage. All of this applies to firing normal non-corrosive smokeless ammunition. IF you used blackpowder loads, be double SURE to clean with hot soapy water and then using normal solvent/oil afterwards to prevent corrosion.
HTH
John