Hi @IndependentHare : I don't know exactly what your model is (beyond the general "mixed" descriptor). But. generally speaking, the answer to your question "Does this mean the Least Squares Means plot I am seeing does not incorporate my random effect "ID" into the plot?" is "no". The random effects are incorporated via incorporatiing/accounting for/etc. varibility between IDs. Again, it will depend on your model, but generally speaking the standard errors (and therefore confidence intervals) for your treatment comparisons account for variability between IDs. You can see this via making your ID factor fixed (or ignore ID completely) and comparing the results with your mixed model results.
And welcome to the community!