Trending @Capgemini; Is early release possible?

I currently hold an offer with a new company, they want me to join in less than 60 days. Can I negotiate for an early release?

I'm currently working on a support project. If my manager agrees, is that possible?

I also read the offer letter which says "In lieu of notice". If I'm ready to pay the notice buyout amount in case my manager and HR reject my request, will that work out?

Can someone please shed some light on that? I've got this offer after months of struggle, I don't want to lose it.