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... is lawnmower grammatically correct or should it always be lawn mower?
Hello Mower freak. blush
From my understanding both are correct.
It's part of the history of the malleability of the English language.

Here's a clear explanation: -
https://www.sarahtownsendeditorial....-one-compound-words-and-how-to-use-them/

I'm happy to use lawnmower and grasscatcher and the like.
For me, they are closed compound words.
Or, is that closed-compound words? grin

Cheers
Jack