Fractal-grid-generated turbulence is a successful technique to significantly increase the reaction rate in the center of a low-swirl flame. Previous results (Verbeek et al. Combust. Flame 162(1), 129–143, 2015) are promising, but the experiments are only performed using natural gas at a single equivalence ratio and flow rate. In industry, the need arises to adapt gas turbines to a wider range of fuels, such as biogas and syngas. To simulate these other fuels, natural gas is enriched with up to 30 % hydrogen (molar based). By means of planar OH-LIF, the turbulent flame speed is assessed. It is shown that the beneficial effect of fractal-grid-generated turbulence remains upon hydrogen enrichment. The fractal grids enhance the combustion in an energy efficient way, irrespective of the hydrogen fraction. Moreover, the characteristic linear relation of the normalized local consumption speed versus the normalized rms velocity holds for the investigated range, with an increasing coefficient upon hydrogen enrichment. For industry, a wide operability range is essential to operate at part load, therefore the lean stability limit is investigated, as well. It is shown that fractal grids increase the lean stability limit, i.e., the adiabatic flame temperature at which blow off occurs, by 50 K, compared to a standard grid. Increasing the bulk flow significantly increases the lean stability limit and the difference between the two investigated grid types increases upon hydrogen enrichment. Hydrogen addition results in a decrease in the lean stability limit, regardless of the grid. A positive correlation was found between the adiabatic flame temperature at blow-off and the rms velocity at the flame brush. The outcome of the presented study provides, despite a slightly increased lean stability limit, a promising prospect for the application of fractal grids in industrial low-swirl combustion.