This paper explores the complexity in the connection between city liveliness and land use configurations for housing and consumption amenities. The sources of this complexity are captured by an integrated spatial and temporal non-stationary modelling approach that uses local linear methods to estimate heterogeneous dynamics of the spatial-temporal process. City liveliness is measured by aggregated space-time human activity intensities using mobile phone positioning data from Beijing. We find that the land use configurations for housing amenities contribute little to city liveliness, whereas consumption amenities play a significant role in attracting human activity intensities. However, such effects vary substantially over space and during a 24-hour life span. These results provide the estimates of the changes in hourly human activity distribution that would influence the form of social engagement, development patterns, and public investment policy.