Hi,
Lavaan uses listwise deletion or FIML. This is explained in the documentation of the “missing” argument:
If "listwise", cases with missing values are removed listwise from the data
frame before analysis. If "direct" or "ml" or "fiml" and the estimator is max-
imum likelihood, Full Information Maximum Likelihood (FIML) estimation is
used using all available data in the data frame. This is only valid if the data
are missing completely at random (MCAR) or missing at random (MAR). If
"default", the value is set depending on the estimator and the mimic option.
If you prefer to use multiple imputation, you can do that with the semTools package.
Mikko