Not in any automatic way. There are papers showing how to hack Mplus by making 2 copies of each zero-inflated variable:
- A binary indicator of whether it is nonzero (with NA assigned to truly missing values)
- A continuous indicator of observed nonzero values, which is NA for any observations that are missing or 0
In the Mplus articles, they use marginal MLE to accommodate missingness with FIML, but MML estimation is not currently an option in lavaan. With minimal (true) NAs, I think you might be able to use WLSMV or PML estimation, but I have not seen those evaluated with simulations, so I hesitate to recommend it.
Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam