The imprints of large-scale structures on the Cosmic Microwave Background (CMB) can be studied via the CMB lensing and Integrated Sachs–Wolfe (ISW) signals. In particular, the stacked ISW signal around supervoids has been claimed in several works to be anomalously high. In this study, we find cluster and void superstructures using four tomographic redshift bins with 0 < z < 0.8 from the DESI Legacy Survey and measure the stacked CMB lensing and ISW signals around them. To compare our measurements with ΛCDM model predictions, we construct a mock catalogue with matched galaxy number density and bias and apply the same photo-z uncertainty as the data. The consistency between the mock and the data is verified via the stacked galaxy density profiles around the superstructures and their quantity. The corresponding lensing convergence and ISW maps are then constructed and compared. The stacked lensing signal agrees with data well except at the highest redshift bin in density peaks, where the mock prediction is significantly higher, by approximately a factor of 1.3. The stacked ISW signal is generally consistent with the mock prediction. We do not obtain a significant signal from voids, AISW = −0.10 ± 0.69, and the signal from clusters, AISW = 1.52 ± 0.72, is at best weakly detected. However, these results are strongly inconsistent with previous claims of ISW signals at many times the level of the ΛCDM prediction. We discuss the comparison of our results with past work in this area and investigate possible explanations for this discrepancy.