Yikes, that’s a rough spot to be in.
Unfortunately at the end of the day, if you act un-ethically, even if coerced or told to by your employer/manager - that falls on you. You chose to act unethically and you can not expect to retain any relationship based on your own actions. It would be one thing if your employer had dishonest practices in other areas of the business but you stayed honest.
Every situation is different, but I would hold yourself accountable. If you are being asked to lie or mislead a customer I would reconsider if harming your long term career prospects is worth what may only be a few months of remaining employment with your current employer.
Your reputation will live long past this current job.