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I accepted a lateral offer a few days ago without thinking about my upcoming slate of interviews next week.

At this point, I feel like it would be extremely unprofessional to call and cancel. However, I don’t want to waste anyone’s time.

I spoke with a mentor of mine and he mentioned that, sometimes, conflicts arise, so waiting those potential offers out may not be the worst case scenario.

Just looking for general advice.

It would be prudent for you to do the interviews if you think there's any risk that your current offer could fall through, so that's probably the best outcome.

If you think the interviews are a waste of time, no one will mind if you cancel. It's not unprofessional to cancel an interview because you're no longer interested in the job.