What is this liriope looking plant?
Your question' better suited to Gardening SE where members can identify plants. As it is, I'm an active member there and the identity of these flowers are straightforward. They're all different cultivars of the daylily (plants in the Hemerocallis genus). If you use Google image search, you'll see photos of various cultivars. Basic structure:



Notice the flowers on a branched (or unbranched) scape (tall stem); leaves arise from the base of the plant. Flowers can be single or double (sometimes more); single flowers (as in your lower left photo) have six petals.

While Asian and Oriental lilies are toxic to pets (even the pollen is toxic to cats if they lick it off their fur), daylilies aren't. They're easy to tell apart as the daylily has long narrow strap-like leaves with flowers on stems with no leaves. Asian and Oriental lily have small leaves continue up the length of the stem like this - 


This includes Easter lilies.

Daylilies are named for the reason individual flowers lasts only one day. But each stem has many buds on it that continue to mature over a few weeks so will produce flowers for about a month (as some stems don't have open flowers yet when the first stems start flowering).