Does this sound natural?
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"When I got home, my dog happily wagged her tail, ran towards me, and put her paws on my legs asking for my lap. I pet her on the head and said: "who's a good girl? Who's a good girl?". Then she laid on the floor and asked me to rub her belly like she usually does"

See a translation

“her paws”

“petted her” (since the rest of your sentence is past tense)

Technically, the past tense of “lie down” is “lay down” (not to be confused with the present tense “lay down”).

• Lie down (present) = to put yourself in a horizontal position
• Lay down (present) = to put down an object
• Lay down (past) = past tense of lie down
• Laid down (past) = past tense of lay down

However, this would sound weird in real life. Most people say “laid” like you did because it sounds better, even though it’s not technically correct. Just wanted to point it out so you know!