In the scenario your describe, the model you propose wouldn't work. Although you have multiple observations of predictors over time for each individual, you only have 1 outcome observation for each individual. The model wouldn't have enough information to distinguish residual error (predicted versus observed outcome) in the model itself from differences among the individuals (variances among individuals' intercept values, in your model). Depending on how you set up the data and the model, you would either get error messages like "Error: number of levels of each grouping factor must be < number of observations" or a model that is essentially unidentifiable.

In your scenario of multiple predictor observations over time prior to the single outcome observation, you wouldn't necessarily need to correct for correlations among the predictor observations. You could think about those 3 blood pressure observations similarly to how you might think about 3 different types of measurements (e.g., blood pressure, total cholesterol, and hemoglobin A1C) as predictor variables in a model of a single outcome. Yes, those variables would be correlated within any individual, but with only a single outcome observation there isn't any correlation among outcomes (maybe better, correlations among residuals) to handle with random-effect terms. Depending on the details, you might consider working with robust standard errors.

There is a situation related to your scenario that would call for a mixed model, however. There are joint models that combine mixed models of predictor variables over time along with time-to-event modeling, in which the values of those predictors are associated with the risk of the event. Typically, the instantaneous values of the predictors are associated with the instantaneous event risk. This type of model can provide continuous estimates of the predictors to inform the event analysis and smooth out imprecision in measurements of the predictors. Note, however, that the "predictor" variables for the event analysis are then outcome variables in the model of their trajectories over time.