Is it not just a blockchain slapped on top of the slower blockchain?
Once the channel is set up on the blockchain between two users and has some amount of bitcoin committed to it, the participants can securely transact between each other with only private communications between each other, without requiring transactions in the blockchain. When either user is done with the channel, either of them may broadcast the settlement transaction which withdraws the committed funds in the correct amounts to each participant. (Every time the participants make a transaction between each other, they create create a new settlement transaction, and a separate transaction which invalidates the previous settlement transaction. These are regular Bitcoin transactions, but they're held privately by the participants instead of being broadcast on the blockchain immediately. If either of the particpants tries to broadcast an earlier version of the settlement transaction, then the other participant can broadcast the invalidation transaction within a certain pre-agreed time, which rewards them the funds as punishment to the defector.)
Then the real fun comes from the "lightning network" part: if Alice wants to send funds to Charlie but has no open lightning channel to Charlie, but she knows that both her and Charlie have an open channel with Bob, then she can do an off-chain lightning transaction through Bob to Charlie, without any risk of Bob taking the funds for himself.
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/
And secondly, frankly, I think Bitcoin dreadful for micropayments. It's really hard to get hold of for most people, requiring all sorts of setup and accounts.