In an EPC-lump sum project where contract duration is extended, contractor's insurances is one of the responsibility of the contractor. Does the additional cost in extending the insurances be raised as claim in the project lump sum contract value, or be a sole responsibility of the contractor?

The contractor will have an annual insurance cost for their yard.  In a lump sum contract with a defined project duration, the contractor will build a portion of this annual cost into the contract value to recover the cost, under preliminaries/overheads.  If the contractor is entitled to an extension of time, where the Client is liable for the prolongation costs, then the contractor is entitled to charge additional costs for the insurances, commensurate with the additional time being added to the Project schedule.

As with all claims, they should be fully supported with appropriate evidence, but in principle this is not an unreasonable thing to expect from the contractor.

i believe as it is lump sum project. therefore its the sole responsibility of the contractor 

the insurance is contractor headache to fullfill their client approved extended date but we can claim some money from the preliminaries running cost like engineer facilities,salary,maintenance for any items to keep our comapny cash flow.

If the provisional extension granted due to clients delay then contractor has a right to demand

it should be a sole responsibility of the contractor. the contractor should include the value of the insurance in their proposal costs.

Contract duration shall be extended due to various reasons, but if it is extended due to client request we can include our additional price of insurance in our costing.

you can try other expenditure as insurance

The Contractor shall claim for the additional cost incured on the premium paid for the insurance on the extended period of time, provided the delay in completion is not due to the Contractor. 

Client should request the contractor to upgrade the insurance bond to cover the re-evaluated cost of the project lump sum, as a separate claim, no need to be included in the lump sum, usually