and places like Lyon (from Lugdunum, Fortress of Lugh)

True.

London (also meaning Fortress of Lugh) are named after him.

Nope. < Londinium < lond-. Error 404, velar not found.

Wikipedia has an extensively cited discussion about London's etymology.

'Log' is Irish for 'hollow'. A certain spot in the headwaters of the River Ayr in Scotland is called 'Logan' from this root and gives us the given name Logan.

Unfortunately those words are loanwords from Latin locus it seems.

'Loch' means lake, the connection being quite clear. In fact both are from Proto-Indo-European laku.

AFAIK it is more likely to be *lókus.

So my question is, are these words related? Loch and Lug are both elements common to a wider cultural sphere of Western European, so a connection would seem likely. In some traditions, Lug was the only survivor of three sons thrown into a whirlpool; perhaps a case is to be made that his name comes from the word 'lake'? What I cannot find is where, if at all, 'log' fits into all of this. As I understand it, the word refers to a cavity in a tree, and I can't find any similar words or notions in other languages.

"log" has been ruled out, so now let's deal with "Lugh".

Lugh has been reconstructed to *Lugus and lochs have been reconstructed to *loku(s)... yeah there's no connection.