Can Lightning Network be used for individual small transactions?
Yes, LN would help you directly.

Suppose you have an open LN channel with Shapeshift or are able to route a payment through LN (i.e. you have a channel open with someone else who has channels to other people). Suppose that IOTA also has implemented LN and you have an open payment channel on IOTA. Now when you want to exchange BTC for IOTA with Shapeshift, you would route your payment through LN to Shapeshift and they would then route a payment on IOTA through IOTA's LN to you.

In fact, this could be done as one route with the guarantee that you will get your money and not have to rely on Shapeshift or any other third party. This is known as an atomic swap. LN allows for atomic swaps like this for coins that have LN implemented.

So in this scenario, you don't have to pay a transaction fee to send money to Shapeshift. Instead you paid a transaction fee to open the payment channel which you are using for transacting with many different people, not just Shapeshift.