Is this small dog friendly? like if the dog is being held & sits on lap during the visit?

Seems unlikely. This is an indoor cafe/bakery and probably not a good place for animals.

I have seen dogs tied up outside but never inside the shop.

No...waaaaay too small at Chicago Avenue

No. This is a restaurant with no outdoor seating. That would be the only approved place (patio), if the establishment had the proper permit as well.

I didn't see anything against that when I went there.

got it!