To interact with salesforce you typically need a user (which mostly requires a paid license too). There are rare exceptions like public sites.
So in order to build something using either the Mobile SDK or Lightning, you need a user.
The Mobile SDK is an approach to create native Apps for devices using API to interact with the platform.
The Lightning framework on the other hand will run the App on the platform.
Salesforce seems to push a lot of effort into Lightning and the concept comes with lots of new features and possibilities. So I expect this will be the future. Unfortunately the term Lightning has also been used to rebrand lots of things so maybe it's less confusing to speak about Aura What is the difference between Aura and Lightning frameworks?
If you need an app for your customers (and/or partners) you best have a look at Communities
They also require paid licenses but are cheaper an come in packages.
There are inofficial tricks to implement your own user management based on public sites. This would save you license costs but you also loose a lot of existing functionality and security.