Here is the Lido 14: LIDO 14 sailboat specifications and details on sailboatdata.com
I looked at your profile pictures of the teak CB cap. It is a judgment call you will have to make.
I have repaired some of the teak on my boat using 105/205 mixed with teak sawdust and covered it with Cetol. The patches take on the general color of teak but it is by no means a perfect match and is generally darker then the solid teak. Those cracks or splitting in the one picture worry me a bit but they too could be filled in. How it would end up looking is up for grabs.
Speaking of visual appearance I'd get some teak oil ($10/quart at hardware store) and oil those pieces up. You are right that teak is an oily wood. I believe that the oil helps to protect what solid wood remains. Oiled teak looks much nicer then dry wood, in my humble opinion.
What I think would probably look the best would be if you could get some new teak stock and make new pieces for the most worn out looking stuff. I can get teak wood for around $20/board foot (1 bd.ft.= 1" x 12" x 12"). That means that a 4' piece of 1" x 12" would cost nearly $100, but that might be enough to repair your CB trunk cap. Mahogany would be cheaper (by not that much) and would also look good but it is not as durable in the elements as teak.
I take it that you are not sailing in Casco Bay these days?