First of all, try to capture what you call fungus with a digital camera and show it to us. Why ? Because many late Carl Zeiss lenses for the Contax cameras suffer from edge separation due to a synthetic glue used at the Zeiss Oberkochen plant for the late production batches in replacement of the Canada balsam. So, you may think it's fungus while it's separation actually. What does this problem look like ? A picture will tell it to us. "Zeiss-patented" separation generally looks like large irized stains starting from the glass edges but it may sometimes vary as for its look.
If it proves to be actual fungus, you have several options. If it's some aerobic fungus (generally looking like a black spiderweb starting from the periphery of the glass), it will clean off quite easily with isopropylic alcohol or diluted ammonia peroxyde provided that you can get access to the sick lens element surface. The glass surface will get clean again and remain fungus-free for the rest of your life if you carefully and fully wipe the fungus off and let the lens get well dry before you reassemble.
The other form of fungus (the anaerobic one) is a killer and will have probably etched the glass already. So, trying to salvage the lens is not worth the trouble. You can't fix it. Nobody can unless the glass is cleaned, repolished, and recoated - I would recommend this treatment for a very rare and extremely valuable lens only.
This kind of fungus usually looks like a dense net of filaments spreading all over the glass surface and it may very well start from several places at once - lens center included. I have handled a Canon RF 50/1.8 lens in this condition recently. It was really impressive - the glass facing the aperture blades on the rear group looked like it had been cleaned with sandpaper. The bacterials had randomly etched the glass on almost all its surface.
Since getting a nice and fungus free 135/4 Sonnar in Contax RF mount at auction is very easy, and just because this otherwise extremely sharp and outstanding lens is generally a bargain, here is what I'd do : just have the seller take it back, and move along. Then you can think of getting another one which won't have any problems. Prefer a Zeiss Opton (or even a prewar Jena) Sonnar if you want to be sure you won't have separation problems.
The last option would be to test the lens as it is. You may very well find, that it's sharp and contrasty enough for your needs. If you got it for a few bucks at a flea market, you can live with its quirks until the fungus has grown enough so that the sick lens gets opaque, which will take some decades.
The postwar 135/4 doesn't exactly dismantle the same way the J-11 does. You have to remove the lens mount from the rear in case you want to clean and relube the helical, for example.
Here is a pair of photos taken with a Contax IIa and a postwar Carl Zeiss 135/4 Sonnar - this one thanksfully being in perfect shape. I paid $47 at auction for it two
years ago.
Good luck !
