What does Muir mean?
From Scottish Gaelic 'muir' meaning 'sea' (cognate with Latin mare and Irish muir). Also exists as a Scottish surname derived from a word for 'moor'; the Gaelic sea sense is the water connection.
What does Lyall mean?
From the Old Norse personal name Liulfr, whose second element is 'ulfr' ('wolf'); adapted in Scotland after Norse settlement. The first element is obscure (possibly 'lid', host/people), so only the 'wolf' element is securely attested; a separate Gaelic derivation has also been proposed.