AFAIK that’s as per the design: LKJCholeskyCov can only handle a single covariance matrix (2D, but not 3D).
Also having a different prior covariance matrix for each observation strikes me as having perhaps too many degrees of freedom in the model: like giving each observation it’s own intercept. Would make it hard to generalise (learn) much about the data that way. What’s your model structure such that you need that much freedom?
EDIT for clarity: you can certainly have a different cov matrix per observation, but I dont immediately see where you would need a different prior for each observation: the typical thing would be to give them all the same prior.