This is the 5341st most frequent Japanese word.
lil
The word "lil" is not a Japanese word. It is an English slang abbreviation for "little."
'小さな' in this sentence is interpreted as 'lil' or 'little,' referring to the size and coziness of the shop.
この小さな店は、とても落ち着きます。
This lil shop is very calming.
'リル' serves here as a proper noun, referring specifically to the name of the cat.
リルという名前の猫を飼っています。
I have a cat named Lil.
'リルな' means 'lil' (little) in a casual context, expressing endearing or small-scaled charm.