Merchants transact in fiat,
Most immediately convert BTC to fiat upon receipt making sure they don't lose money on btc instability.
Lightning network is even worse as the time locks insure no quick fiat conversion.
Meaning if a Merchant does use LN, they do it thru a 3rd party service that offers almost instant fiat conversion.
That's basically the same as the current situation: most merchants use a payment processor to take care of the Bitcoin transaction, and get paid directly in fiat. I don't even think the merchant has to choose for LN, once his payment processor accepts it, it gets added just like some merchants accept many different altcoins.