A key challenge in the use of hydrogen in practical combustors is to stabilize the flame at equivalence ratios close and even below the LBO limit. Plasma-Assisted Combustion (PAC) has been shown to improve the ignition, stabilization, and blowout margins of combustion systems for a great variety of fuels. In this work, Nanosecond Repetitively Pulsed (NRP) discharges are applied to extend the lean blowout limit (LBO) of a partially premixed hydrogen-air combustor atmospheric test rig equipped with a special unit injecting gaseous hydrogen in crossflow into a swirling air stream. The plasma is formed between this injector and an electrode placed in the central recirculation zone. The LBO limit of a 2.2-kW, V-attached flame is extended from 0.220 to 0.177 (20% reduction) using NRP discharges with a plasma power of about 1% of the nominal flame power. Spectroscopic measurements indicate that the plasma operates in the non-equilibrium spark regime: a low ionization degree is observed, and the temperature in the interelectrode gap is moderate (3500 K on average). It is found that plasma discharges increase the OH$^∗$ concentration at the flame foot, in the vicinity of the plasma location. Burnt gases analyzed at the outlet of the system indicate that low NO$_x$ concentrations are being produced, even at stoichiometric conditions where the Emission Index reaches its maximum value of 1.1 gNO$_x$/kgH$_2$. The application of the NRP discharges increases the NOx concentration at all equivalence ratios. To minimize the power consumption and the NO$_x$ increase, the NRP discharges are applied with a duty cycle where the plasma is discharged during about half of the time. It is shown that the NO$_x$ concentration scales linearly with the plasma power and thus that NO$_x$ emission induced by the plasma can be mitigated by 60% with this technique while still preserving the LBO extension.