We have observed four low-luminosity active galactic nuclei classified as Type 1 LINERs with the X-ray Telescope (XRT) and the UltraViolet-Optical Telescope (UVOT) onboard Swift, in an attempt to clarify the main powering mechanism of this class of nearby sources. Among our targets, we detect X-ray variability in NGC 3998 for the first time. The light curves of this object reveal variations of up to 30% amplitude in half a day, with no significant spectral variability on this time scale. We also observe a decrease of ~30% over 9 days, with significant spectral softening. Moreover, the X-ray flux is ~40% lower than observed in previous years. Variability is detected in M 81 as well, at levels comparable to those reported previously: a flux increase in the hard X-rays (1-10 keV) of 30% in ~3 hours and variations by up to a factor of 2 within a few years. This X-ray behaviour is similar to that of higher-luminosity, Seyfert-type, objects. Using previous high-angular-resolution imaging data from the Hubble Space Telescope (HST), we evaluate the diffuse UV emission due to the host galaxy and isolate the nuclear flux in our UVOT observations. All sources are detected in the UV band, at levels similar to those of the previous observations with HST. The XRT (0.2-10 keV) spectra are well described by single power-laws and the UV-to-X-ray flux ratios are again consistent with those of Seyferts and radio-loud AGNs of higher luminosity. The similarity in X-ray variability and broad-band energy distributions suggests the presence of similar accretion and radiation processes in low- and high-luminosity AGNs.