A service provider was not able to completely deliver the contract as specified in the Terms of Reference. Further the contract was awarded as one (1) Lot and no breakdown on how much per item. Can the PE process the payment by deducting the undelivered service based on the existing cost parameter or historical data?
No. You said that the award was in lot (lumpsum). It means 1 or 0. Either everything was delivered or nothing. You cannot change that fact after bidding and award. Since there is no complete delivery, there is NO delivery, and no payment is required.
However, under the principle of quantum meruit, the contractor may receive reasonal compensation for the services already rendered, after deducting the applicable liquidated damages.