Lens boards for the older Omegas are still quite available - both new and used from the usual online sources (e.g. Calumet, etc.). The ones I have all have a large center hole, and then a small adapter plate attached with three screws. The center hole in the adapter plate is selected based on the size needed for the specific lens. Some lenses use a 39mm Leica screw-in mount, others a clean hole with a retainer ring on the back side.

You may be able to (carefully) clean the Besseler lens using the usual blow-it, brush-it, lens-cleaner-it technique. If there is dust inside, you may also be able to remove the front element to clean the interior surfaces. That, however, gets a bit trickier, and depends on the lens design. If it is too dirty inside, and you can't get at those surfaces, I'd also suggest getting another lens in better condition.

You are correct about the "silver bucket" being the condenser assembly. There are two large lenses inside that, with the convex surfaces facing each other. The assumbly should be removeable via a couple of side screws at the top, and L-shaped retainer slots. Be careful when you remove it, as the lenses just sit inside, and it's heavier than it looks. You'll want to remove the condenser lenses and carefully clean them with lens-cleaning fluid and a lens cloth. Over time, atmospheric gunk gets on these and substantially reduces the light transmission.

Different condensors are often used for different focal lengths. If you have the D2V model, there is a third condenser lens in a housing below the lamp head, with a flip=up door and slots to reposition the third lens.

There's at least one dealer online that services older Omega enlargers, and has a variety of parts available. A Google search on "Omega enlargers" should turn him up.