We are unfortunately unable to upgrade from this version.
Is there custom YUI code out there that we could implement into Moodle 2.1 that is similar to drag and drop matching for 2.4?
You are mistaken. There never was a drag & drop matching question type for the Lesson activity, but for the Quiz activity.
I would like to develop a lesson question type for drag and drop.
Where is the best place to learn about Moodle development for lesson question types? Which code files within Moodle implement lesson question types? Just having a place to get started would be a plus.