Is it the onus lies on or with?

Excuse me, I'm curious about the phrase "Is it the onus lies on or with?" Could you clarify for me the proper usage in this context? I've heard both expressions used, but I'm not sure which one is grammatically correct and more commonly accepted. As a professional in the field of cryptocurrency and finance, I'm often required to write precise and concise reports, so it's important for me to use the correct terminology. Thank you in advance for your help.