In measurement model, one of the construct having AVE 0.4 but the composite reliability is 1 and Chi square = 1.099, GFI = 0.995, CFI = 0.997, RMSEA = 0.022. So, is it OK to go ahead in SEM.
It is recommended to have AVE value more than 0.5 as per Kline (1998), however, if its 0.4 you must see that the AVE value of the construct is more than Maximum Shared Variance (MSV) and Average Shared Variance (ASV) as recommended by Fornell and Larker, 1981.
I hope it is helpful. All the best for your research work.
This is only recommended for formative predictive models, in SEM models the most advisable is to establish the measurement criteria of the factorial loads, for a dicriminant analysis you can perform an FCA of all the variables with significant correlations.