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Trying to estimate a VAR where I have no autocorrelation and normality in the errors I find that the only way to achieve both
is to have a lag structure that is not continuous i.e. the lag intervals must be 1-10, 36-40. How legitimate is this? is it ok to use
a lag structure like this? Am I missing something?

If your model is for forecasting purposes, then you should include any significant lags (in line with the parsimony principle) to increase its predictive power. However, such a discontinuity in lag specification may not be meaningful if you are looking for a structural relationship. Moreover, please keep in mind that different lag-length criteria produces different results, and lags 36 to 40 may turn out to be not significant at all, if you conduct a more through lag-length analysis.