The Chromospheric Lyα SpectroPolarimeter (CLASP) is a sounding rocket experiment launched on 2015 September 3 to investigate the solar chromosphere and transition region. The slit-jaw (SJ) optical system captured Lyα images with a high time cadence of 0.6 s. From the CLASP/SJ observations, many variations in the solar chromosphere and transition region emission with a timescale of <1 minute were discovered. In this paper, we focus on the active region within the SJ field of view and investigate the relationship between short (<30 s) temporal variations in the Lyα emission and the coronal structures observed by Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA). We compare the Lyα temporal variations at the coronal loop footpoints observed in the AIA 211 Å (≈2 MK) and AIA 171 Å (≈0.6 MK) channels with those in the regions with bright Lyα features without a clear association with the coronal loop footpoints. We find more short (<30 s) temporal variations in the Lyα intensity in the footpoint regions. Those variations did not depend on the temperature of the coronal loops. Therefore, the temporal variations in the Lyα intensity at this timescale range could be related to the heating of the coronal structures up to temperatures around the sensitivity peak of 171 Å. No signature was found to support the scenario that these Lyα intensity variations were related to the nanoflares. Waves or jets from the lower layers (lower chromosphere or photosphere) are possible causes for this phenomenon.