Stiff shower lever

ck7ah

Hi
I am not sure what the thing in the red circle is called (the part that you lift up on the tap for the shower to come on), however its very stiff now and i was wondering how i could clean it or would it be better to replace the taps are they are over 10 years old?

ThisIsWeird

The diverter valve.
If the rest of the tap is in good order, then you should be able to remove and dismantle the valve with the main tap body left in situ.
It'll then be a case of cleaning up the parts, liberally coating them in silicone grease, and - quite possibly - having to replace some rubber O rings. 
I did this exact job on my own bath mixer earlier this year, and bought a wee bag of mixed-size rubber O rings from eBay for a couple of squid. Very therapeutic, and it now works better than it did when new. 
The issue with mine was that it dribbled water from around the knob (a lever) when on shower position, and I found that a couple of O rings were completely mangled/perished inside.
Your call - £5 in parts, or ~£200+
Do you know the make and model - is that pic of the exact one? I'm guessing, but suspect the knob will be held on with a grub screw through the side, and removing it will expose a nut which will then unscrew the whole valve assy. Or possibly it can be unscrewed and withdrawn from the underside, once the hose is removed.