Can we have NAs (missing data) in a linear-mixed model? I've kinda asked this before, but I guess that I've made it too complicated and I still don't get it right...(I'm using R, so lmer)

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*To put it simply: can we have NAs in the outcome and/or in the predictor variables of a linear mixed model (or should we always delete them or imputate?) So,

1) Can we have Na/missing data in the outcome variable?
2) Can we have NA/missing data in the predictor variables?
Thanks in advance! (I'm trying to understand if a model (not necessary mine) with Nas is conceptually wrong + how having Nas bias the results in general so that I can get the bigger picture)
edit:
I'm wondering If I should do this before (any) model:
data <- data %>% 
  dplyr::select(Participant, OutcomeContVariable, PredContVariable, PredCateg2-LevelVariable) %>% 
  # group_by(Participant) %>% 
  # filter(all(!is.na(OutcomeContVariable) & !is.na(PredContVariable)))


Part 1 of the question
For the outcome variable, if one does not explicitly impute missing values (whether you leave records with NA in or delete them, as long as you leave the non-missing records for patients with partially missing data in), then missing values would be dealt with under full information maximum likelihood. I.e. using a mixed model without imputing missing values is usually equivalent to imputing under the assumption of missing at random.
For example, if you have a randomized trial comparing two treatments and values after treatment discontinuation are missing, then you are saying that your estimand is: the hypothetical difference between treatments if all patients had finished treatment (which we know they have not, but you are interested in this hypothetical question). Additionally, you assume that everything that explains the treatment discontinuation is part of the baseline covariates in the model or is jointly modelled together with the outcome variable in your outcome model.
If you want to target a different estimand or want to not make the assumption above, you would want to explicitly impute (usually done via multiple imputation) under whatever assumptions you want to make.
Part 2 of the question
lmer has no capabilities for directly dealing with missing covariates, but that's not a general theoretical limitation (e.g. in the brms R package you can directly deal with this situation under certain assumptions).
Multiple imputation before model fitting is one of the obvious approaches for dealing with this situation in a way that then lets us use lmer.
