That's not true. By locking funds into a Lightning Network payment channel you solve the double spend problem _in the channel_ (the person receiving your payment knows that in order for you to double spend the channel, the payment recipient would need to approve the double spend). The risk of being double spent still exists on the underlying blockchain though, which is solved with a smart-contract structure that allows the counter party to the perpetrator of fraud to revoke a fraudulent double spend.
This process effectively doubles the required amount of transactions and time spent for the 'lightning' transaction to take place?
Lightning is exactly the same way. You set up a contract with the payment processor. This requires the transaction to be accepted into a block. Then you make as many smaller transactions (which require no blockchain transactions) with the payment processor as you want. At any time, the payment processor can terminate the contract by cashing in the amount of money you have spent. This requires a transaction to be accepted in the block chain. After that the channel is closed and only the amount spent is transferred (the remaining amount is freed up). If it goes beyond the contract length without the payment processor cashing in, then the contract is cancelled and the total amount is freed up.
So basically it allows you to make many transactions through a payment processor, while only making 2 transactions on the block chain. Anyone can be a payment processor, but the protocol requires the payment processor to have capital equal to the transactions in process (they have to transfer funds to a third party before they get paid -- although they are guaranteed to get paid by the end of the contract).
It's actually a pretty slick protocol. Their website has a video with implementation details that explains exactly how it works: https://lightning.network/