Let’s talk about terminology.
Capacity: The number of transactions that can be processed on the network.
Scalability: Capability of the network to handle a growing amount of work.
1) A 2MB hardfork is a capacity increase but not a scalability improvement.
2) Segregated Witness is a capacity increase and a scalability improvement.
3) Monero has no block size limit and thus a higher capacity than Bitcoin, however its TXO pool is unpruneable, its blockchain would grow faster at same usage, and its transactions take more computational effort to validate, so it doesn’t scale as well as Bitcoin.
The Lightning network is not a sidechain.
A sidechain relies on its own blockchain which is coupled to the Bitcoin blockchain via a two-way peg.
On the other hand, Lightning network consists of native Bitcoin 2-of-2 multisig transactions.
When two Lightning nodes open a payment channel, they both send funds to one multisig address and each provides the counterparty with a pre-signed exit transaction. If a party wants to resolve the payment channel, they can unilaterally add their own (the second) signature and send the transaction to the Bitcoin network for confirmation.
However, it is more efficient to update the balance of the payment channel repeatedly by exchanging new exit transactions. The updated exit transactions simultaneously invalidate the previous exit transaction. Whenever anyone wants to get out or tries to cheat (by using an invalid exit transaction), the exit transaction is moved to the Bitcoin blockchain for arbitration. Newer exit transactions then override older ones.
So, while Lightning Transactions can happen off-chain, they can be put on-chain anytime.