I know "He was junior to me in high school" works.
"He was a few grades behind me in high school" or "He was a few grades lower to/than me in high school"?
Are any of these natural?
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In my area of the United States, "He was below my grade" or "he was behind me" would be more natural — but even those are a bit unnatural. From the perspective of someone in the twelfth grade referring to someone in the tenth grade it would be natural to say...
In other words, it's more natural (in my area) to refer to the specific grade (an absolute reference) rather than the difference in grades (a relative reference).
But, if you're specifically asking for a phrase that would be used by one adult referring to another adult (both of whom have graduated), then it would be natural to say, "he was a few grades behind me."