Context. Radio recombination lines (RRLs) at frequencies ν < 250 MHz trace the cold, diffuse phase of the interstellar medium, and yet, RRLs have been largely unexplored outside of our Galaxy. Next-generation low-frequency interferometers such as LOFAR, MWA, and the future SKA will, with unprecedented sensitivity, resolution, and large fractional bandwidths, enable the exploration of the extragalactic RRL universe. Aims. We describe methods used to (1) process LOFAR high band antenna (HBA) observations for RRL analysis, and (2) search spectra for RRLs blindly in redshift space. Methods. We observed the radio quasar 3C 190 (z ≈ 1.2) with the LOFAR HBA. In reducing these data for spectroscopic analysis, we placed special emphasis on bandpass calibration. We devised cross-correlation techniques that utilize the unique frequency spacing between RRLs to significantly identify RRLs in a low-frequency spectrum. We demonstrate the utility of this method by applying it to existing low-frequency spectra of Cassiopeia A and M 82, and to the new observations of 3C 190. Results. Radio recombination lines have been detected in the foreground of 3C 190 at z = 1.12355 (assuming a carbon origin) owing to the first detection of RRLs outside of the local universe (first reported in A&A, 622, A7). Toward the Galactic supernova remnant Cassiopeia A, we uncover three new detections: (1) stimulated Cϵ transitions (Δn = 5) for the first time at low radio frequencies, (2) Hα transitions at 64 MHz with a full width at half-maximum of 3.1 km s⁻¹ the most narrow and one of the lowest frequency detections of hydrogen to date, and (3) Cα at v_LSR ≈ 0 km s⁻¹ in the frequency range 55–78 MHz for the first time. Additionally, we recover Cα, Cβ, Cγ, and Cδ from the −47 km s⁻¹ and −38 km s⁻¹ components. In the nearby starburst galaxy M 82, we do not find a significant feature. With previously used techniques, we reproduce the previously reported line properties. Conclusions. RRLs have been blindly searched and successfully identified in Galactic (to high-order transitions) and extragalactic (to high redshift) observations with our spectral searching method. Our current searches for RRLs in LOFAR observations are limited to narrow (<100 km s⁻¹) features, owing to the relatively small number of channels available for continuum estimation. Future strategies making use of a wider band (covering multiple LOFAR subbands) or designs with larger contiguous frequency chunks would aid calibration to deeper sensitivities and broader features.