intention to treat with missing outcomes in longitudinal data In an ITT randomized trial, there are one baseline response (y0) and 5 post-treatment follow-ups (y1...y5). Although the number of post-treatment follow-ups is predetermined, participants can drop out of the study. So, for example, ID 1 has responses y0, y1, y2. ID 2 has responses y0, y1, y2, y3, y4,y5. ID 3 only has response y0. I am planning to use linear mixed model for analysis.
In that case, do I need to impute the missing responses for each participant e.g. via last observation carried forward? Or no imputation needed for people who had at least one post-treatment response, which already satisfies the ITT requirement?
What if the missing response is at baseline, is multiple imputation the most common way?
 A: 
In that case, do I need to impute the missing responses for each participant e.g. via last observation carried forward?

No. There is no need to impute missing data prior to using linear mixed effects models. Imputation by last observation carried forward is also rarely appropriate.
Note that linear mixed effects models will provide unbiased treatment effect estimates provided that data are missing at random. In other words, whether a data point is missing depends only on previous observations and/or model covariates. This may not be the case, for example, if people tend to drop-out because of a sudden worsening of symptoms.

What if the missing response is at baseline, is multiple imputation the most common way?

Presuming that you are including baseline score as a predictor (i.e., the RHS of the equation), multiple imputation seems to me an appropriate option (presuming only few are missing their baseline score). This way, everyone with outcome data is included in the analysis (satisfying ITT), and the uncertainty in imputed baseline scores is properly accounted for.
EDIT: First hyperlink went to wrong place. Now corrected.
