"This lie has been spreading by them over the years" is correct

As a UK speaker either ending is fine, but the start should be
This lie has been being spread by them....
or
This lie has been spread by them......

That passive verb formation is tough. I would go with:

They spread this lie over the years.
They spread this lie over many years.

So would I.

now what would you do with that sentence. You have no need for it do you?

Dunno. Haven't worked out the meaning.

Active: somebody does something
"Avoid using the passive voice." - active - subject: you (imperative) - verb: avoid

Passive: something is done - (by whom may or may not be emphasized)
"Use of the passive voice is to be avoided." - passive - subject: use or using (gerund) - verb: some form of to be

The proper verb form for your sentence is "has been spread".