Is there a way to submit assessment attempt information to the LMS and trigger a failed completion after three attempts?

Most often this kind of thing is part of your LMS functionality. It is common to (for example) allow 3 attempts and then lock the course down after a third unsuccessful attempt, redirecting the learner to remedial material or alerting a manager/training department. But this is a function of the LMS, rather than the learning content.

By recording the actual pass/fail status along with score for all three attempts you are able to gain insight as to the learner's progress that you might not otherwise have.