In general, anomalies of subsurface temperature move from west-to-east along the equatorial Pacific.  So, if your heat content index is shifted westward of another index, then there will likely be lead-lag correlations.  In general, oceanic Kelvin waves take ~2-3 months to cross the Pacific and are one of our predictors for ENSO (not our only one!). 

Your caveats are spot on.  Taking in account sample size and using multiple datasets are excellent practices to follow.