You are seeking advice: 'Can my company stop me from going through the buyout process?' They can, for reason or no reason, is the answer. Since the company is your employer, the appointment order states that the employee has to serve the notice period 'and/or pay salary in lieu of notice period.'
Understanding Notice Period Clauses
The first choice is to serve the notice period. The connecting link is 'and/or.' While 'and' is conjunctive (meaning both parts are to be read together), 'or' is disjunctive (meaning it is in the alternative). The intention of the clause does not seem to be to interpret as 'and' but to emphasize the preceding part. So, serving the notice period is the first requirement, and only upon failing to do so does the second part, i.e., the buyout provision, come into play.
Implications of Not Serving Notice Period
Even in normal circumstances, the employee cannot relinquish all duties one fine morning and walk off by just paying off the notice period. This would seriously impair the functioning of any establishment.
Finding a Mutually Satisfying Solution
So, taking the overall situation into account, decide how long you can serve the organization and offer to pay for the remaining period. It is better to work out a mutually satisfying solution rather than insisting on one-sided interest.