Can Lightning Network be used for individual small transactions? Today I went to use shapeshift.io to trade some BTC for IOTA. I only have a small amount of BTC, and I will only be performing a single transaction. Due to congestion on the network coupled with impractical fees the aforementioned operation is infeasible. 

My question is, in theory, does the lightning network help me in this situation? 

I get that it can help me pay merchants several times without bloating the network/incurring multiple fees, but does it help an individual user in a single transaction like the one above? I feel like I'm missing something, because lightning is supposed to solve both congestion and fees, but in my limited understanding, it seems to do this only indirectly. It clearly would unclog the mempool a great deal, and thereby, because of a decrease in congestion result in a concurrent decrease in transaction fees. Right? But is there a direct application for single transactions not involving multiple small in/outputs like my very real world example above?

Thanks a lot for your responses.
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.