Why are you using a framework along with a premium template?
Just use one or the other, and use the simple child theme generator at GPP if you don't know how to create a child theme:
https://graphpaperpress.com/wordpress-child-theme-generator/
Under parent theme select 'I don't see my theme here' and in the box that pops up just type in "lms" (without the quotation marks).
Upload the child theme zip you've created, activate it, and you're good to go. It's important to note that you'll possibly lose the changes you've already made to LMS using the customizer.
If I'm not understanding your question please explain why you require your own custom framework. I don't understand why you'd pay for a premium template, then couple it with your own framework. It's already built on a responsive framework...