Can I ask one of my sister's best friends on a date?
What do you like about your sister's best friend?
I hear that she's very loyal and she has a plain style to her.
If you like her and she likes you, I don't see an issue. You could run the idea past your sister if it would put you more at ease. It's nice of you to consider her feelings in a situation where you're really not required to do so.
Thanks for your imput!
In the end, what matters the most what her friend thinks. If she is attracted to you and likes you, then you should give it a go and ask her out.