This study conducted a detailed examination of seismic vulnerability across different limit states for Schwedler single-layer lattice shells with differing rise-to-span ratios. A comparative analysis of seismic intensity measures, particularly those centered around Sa(T1), was performed to evaluate their effectiveness in vulnerability analysis. To comprehensively address the inherent uncertainties in seismic actions, the study selected a dual set of ground motion scenarios, encompassing both far-field and pulse-type near-field events. A novel approach was employed, integrating a multi-indicator seismic performance assessment model based on the residual seismic safety framework, aiming to thoroughly quantify the cumulative seismic damage to lattice structures. Utilizing the multiple stripes analysis technique enabled the efficient generation of analytical results for vulnerability assessments at various damage thresholds. The findings revealed that lattice shells with larger rise-to-span ratios exhibit increased seismic robustness, notably with far-field seismic events causing more significant damage than their pulse-type near-field counterparts. Furthermore, the study determined that employing seismic intensity measures which consider the effects of higher modes significantly reduces variability in the vulnerability analysis when dealing with pulse-type near-field seismic activity. As a result, the use of the seismic intensity measure IM123 is recommended for assessing the vulnerability of lattice shells with varying rise-to-span ratios, under both far-field and near-field seismic conditions.