Does anyone know where i could purchase a day lily named "Chautauqua Lipstick "?

Not sure that anyone sells that hybrid. Many of the hybrids are personal projects and not produced. The parent plants are Strawberry Velvet × Millie Schlumpf. Maybe you could hybridize it yourself?

Daylily (Hemerocallis 'Chautauqua Lipstick') is an older daylily, not hybridized by anyone with an online presence and as mentioned, most likely by a personal gardener.
Crossing the exact same parent plants would not produce the same plant.

Thanks for the info, @Calif_Sue! I haven't gotten into the world of hybridizing yet. I let my pollinators do all their work naturally! It also explains why my own daylilies have some unique new colors each year.

Thanks to you both, I'm so new with these types of day lilies I appreciate your input.

@Gsdean53 Welcome to the forum : )
You're in good hands here...

[Run, or else you'll own 500+ daylilies and start breeding them and tear out your lawn for more beds, and trade with people online, like some sort of grown up trading card game, except it takes up way more room and refrigerator space and baggies and mini-blinds, and organza bags, and Gain fabric softener and markers, beads, paper clips, Solo cups, dirt, seedling trays (what am I forgetting?)....]

So, yeah, welcome!

Chautauqua Lipstick was hybridized by Harold Nass from Westfield, NY. His last registrations appear to be in 2014 so not that long ago. Searching finds mention that he and his wife Janet have retired and closed their garden. This link from AHS Region 4 shows them listed in the Upstate NY section as being members of BADS, Buffalo Area Daylily Society. Another member Brent Ross, Cottage Gardens, does list a few of their daylilies in his 2019 price list. You could try to contact Brent to see if he knows anyone in the club who may own Chautauqua Lipstick or where you might be able to find it.
http://www.ahsregion4.org/page...
http://daylily.net/gardens/cot...

Gsdean53, good luck with your quest.

Thanks to you all. Char I appreciate all the information. I actually have a friend from my hometown who has over 400 daylilies! Was in touch with her for info and she offered me some of her Chautauqua Lipstick, among a few others I ended up bringing home! So excited in getting started with these beautiful plants!!

That's great news! Very happy to hear you found it.

@Gsdean53,
I'm happy that you were able to secure a few fans of Chautauqua Lipstick. Be sure to add a photo to the database when you get blooms. We would love to see it!