I volunteer on a 17th C recreation sailing vessel and we do not paint, tar, the deadeye lanyards. Yes, we're using synthetic rope, but I've never heard of lanyards being coated on any vessel. Lanyards have to be able to run thru the deadeyes like any other piece of running rigging. Yes, the natural fiber used during the age of sail would be more susceptible to rot without tarring, but then all the other running rigging would face the same issue. I assume running rigging was simply replaced more often than standing rigging. BTW, we do paint the ratlines as they are static.