Hilary Duff, in the first photo above, checks out Lola's anus, perhaps asking herself, "Now where'd I put that stash?"
The second photo, and the third in-text photo taken on the set for the music video Fly (2004), is of her dachshund Chiquita.
I assume Chiquita part chihuahua because she doesn't look like a full blooded dachsy and dachshund ears don't stand up like that.
In the pair of photos below we see HIlary with Lola on the left, and with Lola and Coco on the right. Coco looks a lot like Lola, but has the paler nose.
I don't believe Coco is at all the same as the chihuahua Coco Chanel who belonged to Hilary and Haylie's grandmother, and whom the sisters inherited. I could be wrong, but I think Coco Chanel is a much older, brown chihuahua (seen on Hailey's page to follow).
Hilary generally spells her name with one "L" though it is often seen with two even on publicity releases generated by her promoters. Her first starring film role was in The Soul Collector (1999), a supernatural telefilm with a plot that closely resembled Brad Pitt's Meet Joe Black (1998) but for a younger audience.
She was a big hit on the Disney Channel series Lizzy McGuire from which a feature film was spun in 2003, and is seen regularly in television dramas and feature films, including forthcoming The Story of Bonnie and Clyde (2010) in which she plays Bonnie Parker.