Is it true that gravitational lensing only occurs for objects made of plasma?
Most of space contains a plasma, or at least some ionisation, at some density or other, making the claim hard to dispute at that level. Also, gases and/or plasmas will tend to exist with higher densities in deeper gravity wells.
What is the merit of claim that bending could be caused by plasma and not by gravity?
In general it is possible for light paths to be changed by interaction with matter (a glass lens being an obvious example). In principle similar distortion could happen with a rarefied plasma over large distances. A density variation at the right scale, and with a simple shape would be required.
I expect however that the claim in the link is just a conjecture/challenge, and not mathematically or scientifically robust (although I don't personally have the knowledge and skills to assess that). I suspect that the lensing seen in an Einstein ring would be very hard to duplicate using realistic values for plasma density near the lensing object.
To me, there are plenty of warning signs that this is a crackpot claim from the link. Unfortunately the world is full of them. Often such people cannot be corrected by scientific evidence, in fact they will self-promote that there is "controversy" when engaged in conversation, or complain of being "suppressed by the establishment" when ignored. I am not saying those thing apply to the author (I have not checked other publications), but I would be wary of the "a NASA physicist" label - it is likely correct on some technical label (he worked for NASA and has a qualification in physics) but is not particularly meaningful.
It doesn't help the lay audience (NB I include myself here) when real scientific controversies and useful scepticism can follow a similar pattern. Popular proponents of badly-thought-through or outlier theories often manage to pick up on the form of this and produce "science-y" work, making it harder to filter out good from bad.
Update: I have struggled through a few pages of http://www.extinctionshift.com and stand by this - the work appears to be random picking of equations plus handwaving arguments about how they connect. Nothing is properly analysed.
Does this mean general relativity is invalid?
No, even if somehow the claim had merit, there is plenty of evidence for GR outside of gravitational lensing.
For example: Time-dilation effects of general relativity can be measured directly by atomic clocks. They have got so accurate that we can actually measure the time dilation of a few metres height difference at ground level. The GPS system needs to account for this effect.
It is well known that General Relativity and the Standard Model of quantum mechanics, although our best current models in physics, cannot be the last word. They are not compatible, and where they overlap (typically when considering cosmology or black holes) there is a need for a combined or replacement theory. That doesn't make the theories "wrong" any more than Newtonian physics was "wrong", but it does mean we can expect some extensions or a deeper theory to emerge at some point.