"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.