I'm not a native, but lived in the US for a quarter century. I think you're correct that that "lagged behind" is the correct version, but if you replaced "lagged" with "trailed" it would also be correct without the "behind". Language is very fluid and always evolving, so using "lagged" as one would previously have used "trailed" may soon be considered correct usage.

Note also that these aren't really questions of grammar (syntax) but meaning (semantics). Does "lagged" mean the same thing as "trailed" in this kind of construction? It didn't some decades ago, but maybe it does today. Or will tomorrow.