I don't think it starts with
Ll - see the birthplace column for lots of
Lls for comparison.
Census ref is RG09/4117/17/6
It looks like a house name, every house has a different name.

EDIT: From my vast knowledge of Welsh

"fach" means little.
I notice that next door is Waslodwen - compare the
W with that for
William - so it's Waslodwenfach
