"Way out at sea" meaning

Solution 1:

This is an informal usage of "way" as an adverb: it means that the lighthouse is a long way out at sea. You could think of it as equivalent to the word "far". (Personally I think "way out to sea" reads a bit more nicely).

from https://dictionary.cambridge.org/dictionary/english/way :

way
adverb
UK  /weɪ/ US  /weɪ/
way adverb (EMPHASIS)

informal
used to emphasize degree or separation, especially in space or time:
*After the third lap, she was way behind the other runners.*
*She spends way too much money on clothes.*

For the text as a whole, imagine a comma after "understanding": understanding is a part of the previous phrase, like so:

"Butler felt to me like (he was) a lighthouse blinking from an island of understanding, (which was) way out at sea."

The lighthouse and "island of understanding" are metaphors: they mean that Butler is isolated from others and understands more than others (or perhaps just the writer), and others/the writer just see a glimpse of that understanding when he occasionally communicates it to them.