"Lagged" alone is valid, but it is slightly less clear. Because, while it would be atypical, "X lagged Y" could be read to mean that X caused Y to lag. "X lagge

"Lagged" alone is valid, but it is slightly less clear. Because, while it would be atypical, "X lagged Y" could be read to mean that X caused Y to lag. "X lagged behind Y" removes that ambiguity.