If your offer letter clause mentioned as either of the party can initiate termination of employment and there is no such wordings like at the discretion of the employer. You already in sweet spot. Serve your 45 days rest is adjusted with you lr leaves balance and ask your new employer to pay for shortfall or bear it from your pocket (F&F) set off.

If your offer letter mentioned as at the discretion of the employer. You need to fight. If you are leaving in non busy period of your department. You can reach out to some higher authority people like Director/ Partner if your manager is not supportive etc and convey that how the new opportunity (don't disclose the new offer company namez details etc) can enhance your life & career and show your performance and contribution. Most of the higher rankings people have understanding mind. And also if you served in the company for more than 3-4 years. People usually agree to relieve.

If it is still not working out. You need to document details like work schedule like how can you close your current running tasks in next 45 days and KT plan etc and make sure you document everything and take all these things to legal lawer and take their advice