Suppose in a payment route A->B->C, A desires to pay 0.01 BTC to C. It locks in 0.01 BTC with B in the HTLC having timeout period of say 2 days and B locks 0.01 BTC with C in HTLC having timeout period of 1 day. Now can something like this be done that if C delays in revealing the preimage say takes 1/2 day, then it gets 0.005 BTC and 0.005 BTC is returned to B. Can the contract support such dynamic settlement of payment based on amount of time lost? In the worst case, if C doesn't respond then B gets back full 0.1 BTC.
Such a functionality is currently not implemented and as far as I understand not intended. You can look at Discreet Log Contracts which where intended to solve CFD (Call for difference) contracts for example with cross asset swaps and changing exchange rate within the timelock period. We have a proposal how they could be transfered to lightning. That being said this would mean severe protocol changes and also computation of many signatures. Yet I think a similar construction could be applied for your usecase.