Do Tonearms need servicing

I would say in general, "no". That said you ought to ensure that:
1. your setup/alignment has not drifted out of spec2. the bearings -- if adjustable - are not loose (or tight)
The only wear and tear part is the bearing. If damaged it probably needs factory replacement - or certainly replacement and precision adjustment by someone who doesn't need to ask that question!
Unless it has been abused in some way, i still say "no". I have 30 and 40 year old arms that are un-serviced and work perfectly.

I had my SME V serviced by the manufacturer.  Mainly they upgraded the wires and a few other tweaks.  This was 3 years ago.  They were happy to do the work for a price.  I am not sure they still do this having moved to a place where they only sell tonearms with new TT’s

I had something called a Helius Orion.....needed servicing after a few months.  ...sent it back to England 2 or 3 times then sold it.

Grab the tonearm by the base with one hand and with the other the tonearm tube and giggle it slightly on the vertical than horizontally . If you feel no play or movement your good to go . If there is play in one plane or the other bearings need to be checked . Thats all to it . Rewiring is another thing . 

Another way of checking bearing integrity ( normally the bearings are the only thing that needs to be checked ) is to put the tonearm on zero tracking force and while its floating give it a very slight push . If you see while its moving it gets slightly stuck it needs its bearings to be checked . If it just keeps on moving fluidly bearings normally are ok . Your good to go .

If it's not broken don't fix it.