When multivariate spatial processes have been collected on a regular lattice, the multivariate conditionally autoregressive (MCAR) models are a common choice. However, inference from these MCAR models relies heavily on the pre-specified neighborhood structure and often assumes a separable covariance structure. We present a multivariate spatial model using a spectral analysis approach that enables inference on the conditional relationships between variables that does not rely on a pre-specified neighborhood structure, is non-separable, and is computationally efficient. Covariance and cross-covariance functions are defined in the spectral domain to obtain computational efficiency, and the associated correlation matrix allows for quantification of the conditional dependencies. This approach, along with the traditional MCAR model, is illustrated for the toxic element arsenic and four other soil elements whose relative concentrations were measured on a microscale spatial lattice. Understanding conditional relationships between arsenic and other soil elements provides insights for mitigating pervasive arsenic poisoning in drinking water in southern Asia and elsewhere.