Abstract K2-25b is a Neptune-sized exoplanet (3.45R _⊕) that orbits its M4.5 host with a period of 3.48 days. Due to its membership in the Hyades Cluster, the system has a known age (727 ± 75 Myr). K2-25b’s youth and its similarities with Gl 436b suggested that K2-25b could be undergoing strong atmospheric escape. We observed two transits of K2-25b at Lyα using HST/STIS in order to search for escaping neutral hydrogen. We were unable to detect an exospheric signature, but placed an upper limit of (R _p /R _⋆)∣ _{Ly α} < 0.56 at 95% confidence by fitting the light curve of the Lyα red wing, or < 1.20 in the blue wing. We reconstructed the intrinsic Lyα profile of K2-25 to determine its Lyα flux, and analyzed XMM-Newton observations to determined its X-ray flux. Based on the total X-ray and extreme ultraviolet irradiation of the planet (8763 ± 1049 erg s⁻¹ cm⁻²), we estimated the maximum energy-limited mass-loss rate of K2-25b to be 10.6 − 6.13 + 15.2 × 10 10 g s⁻¹ (0.56M _⊕ per 1 Gyr), five times larger than the similarly estimated mass-loss rate of Gl 436b (2.2 × 10¹⁰ g s⁻¹). The photoionization time is about 3 hr, significantly shorter than Gl 436b’s 14 hr. A nondetection of a Lyα transit could suggest K2-25b is not significantly losing its atmosphere, or factors of the system are resulting in the mass loss being unobservable (e.g., atmosphere composition or the system’s large high-energy flux). Further observations could provide more stringent constraints.