This is a general question (not about the lavaan software) that can be posted to SEMNET:
Fit indices are not very informative. If your chi-squared test is significant and you want to know why, inspect the correlation residuals to see which correlations your model has trouble reproducing/predicting.
If any are > 0.1 in absolute value, most would agree that is a substantial failure of the model, so you could brainstorm about why, and about how your model could be improved. It is possible all the residuals are small, in which case the chi-squared test is reflecting many insubstantial prediction errors that you could argue are not of practical significance. Any single global fit index is incapable of providing such detailed information, and no cutoffs work in general.