We present the first results from the Las Cumbres Observatory Global Telescope (LCOGT) Networks Active Galactic Nuclei Key Project, a large program devoted to using the robotic resources of LCOGT to perform time domain studies of active galaxies. We monitored the Seyfert 1 galaxy Arp~151 (Mrk~40) for $sim$200 days with robotic imagers and with the FLOYDS robotic spectrograph at Faulkes Telescope North. Arp~151 was highly variable during this campaign, with $V$-band light curve variations of $sim$0.3 mag and H$beta$ flux changing by a factor of $sim$3. We measure robust time lags between the $V$-band continuum and the H$alpha$, H$beta$ and H$gamma$ emission lines, with $tau_mathrm{cen} = 13.89^{+1.39}_{-1.41}$, 7.52$^{+1.43}_{-1.06}$ and 7.40$^{+1.50}_{-1.32}$ days, respectively. The lag for the ion{He}{2} $lambda4686$ emission line is unresolved. We measure a velocity-resolved lag for the H$beta$ line, which is clearly asymmetric with higher lags on the blue wing of the line which decline to the red, possibly indicative of radial inflow, and is similar in morphology to past observations of the H$beta$ transfer function shape. Assuming a virialization factor of $f$=5.5, we estimate a black hole mass of $M_mathrm{BH}=6.2^{+1.4}_{-1.2}times$10$^{6}$~$M_{odot}$, also consistent with past measurements for this object. These results represent the first step to demonstrate the powerful robotic capabilities of LCOGT for long-term, AGN time domain campaigns that human intensive programs cannot easily accomplish. Arp 151 is now one of just a few AGN where the virial product is known to remain constant against substantial changes in H$beta$ lag and luminosity.
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