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'LatticeKrig' (LK) is a spatial model that is often used for modeling multiresolution spatial data with flexible covariance structures. An extension to LK under a Bayesian framework is proposed that uses integrated nested Laplace approximations (INLA). The extension enables the spatial analysis of non-Gaussian responses in latent Gaussian models, joint spatial modeling with structured and unstructured random effects, and native support for multithreaded parallel likelihood computation. The proposed extended LatticeKrig (ELK) model uses a reparameterization of LK so that the parameters and prior selection are intuitive and interpretable. Priors can be used to make inference robust by penalizing more complex models, and integration over model parameters allows for posterior uncertainty estimates that account for uncertainty in covariance parameters. ELK's ability to reliably resolve multiresolution spatial structure for pointwise and areal predictions is demonstrated in both simulation study and two applications with non-Gaussian observations: a set of 188,717 LiDAR forest canopy height observations in Bonanza Creek Experimental Forest in Alaska, and a set of 1,612 clusters containing counts of secondary education completion from the 2014 Kenya demographic health survey. ELK has improved central predictions as well as uncertainty characterization according to the considered scoring rules when compared against a number of other models, particularly in the forest canopy height application, and performed faster than LK in our tests in part due to its support for and use of parallelization. [ABSTRACT FROM AUTHOR]