Let's say A merchant is using lightning payment service to accept BTC as payment for his shop. How does existing lightning payment service were able to manage to provide merchant's BTC in form of fiat considering BTC price volatility rate , because at the end of the day merchant needs fiat currency to spend his daily living.
How does existing lightning payment service were able to manage to provide merchant's BTC in form of fiat
Hedging currencies is something that must be performed outside the Lightning or Bitcoin networks.
Exchanging currencies is something that must be performed outside the Lightning or Bitcoin networks.
Some commercial businesses might offer to provide such hedging and/or exchange services but that is separate from Bitcoin and Lightning.
I expect businesses or individuals who are worried about exchange rate fluctuations will often choose to recalculate the prices they offer at very short intervals (e.g. daily, hourly?) and often will immediately exchange received currency they consider uncomfortably volatile for another they consider more stable. Those who are extremely concerned about a specific currency will perhaps choose to transfer all the risk to the other party by insisting on a transactional currency they are comfortable with.