Can Linear Mixed Modelling handle NAs (missing data) in the response variable and/or predictor variable?

I am using the lme4 package and the lmer function in R as I am undertaking linear Mixed Modelling. Is it okay to have NAs in both the response and covariate (predictor) level? I know Linear Mixed modelling excludes the NAs and uses maximum likelihood estimates but I am not sure whether NAs can exist in both the response and predictor variables? If I don't exclude NAs my modelling runs fine but I notice uneven response groups (for the different time points)? Does this matter.

E.g. at baseline (n= 1,980) at 1 month time point (n = 1,841) etc...

Background to my data includes patient data collected at 4 different time points (this is the response variable). There are list of patient characteristics (covariates/predictor variables) included in the model. These include BMI, age, presence of diabetes, blood pressure, radiation dose etc... Some patient data wasn't collected during follow-up so there are missing data (1666) in the dataframe.

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