Context. In the previous decade, two new classes of fast radio transients were detected: the Galactic, rotating radio transients (RRATs) and the extragalactic fast radio bursts (FRBs). If the detectable emission of these objects extends to lower radio frequencies, the LOw Frequency ARray (LOFAR) is ideally suited to seek and localize these transients at frequencies of 10–250 MHz. This is due to LOFAR’s sensitivity, diverse beamform capabilities, and transient buffers for the individual elements that allow post-event imaging of events, potentially at arcsecond resolution. Aims. Our aim is to identify and localize pulses at frequencies below 250 MHz and, in the case of nondetections, derive upper limits on the sky and volume rates of FRBs. Methods. A real-time search program for fast radio transients is installed on the LOFAR systems which runs commensally with other observations, and uses the wide incoherent LOFAR beam (11.25 deg² at 150 MHz). Buffered data from hundreds of dipoles are used to reconstruct the direction and polarization information of the event, and to distinguish between celestial, terrestrial, and instrumental origins. Results. Observations were taken covering either the frequency range 119–151 MHz or in four frequency bands, each of 2 MHz in width, centered at 124, 149, 156, and 185 MHz. A first pilot survey covered a range of dispersion measures (DM) below 120 pc cm⁻³, focusing on Galactic sources, and resulted in an upper limit on the transient rate at LOFAR frequencies of less than 1500 events per sky per day above a fluency of 1.6 kJy ms for an 8-ms pulse. A second pilot survey covered a range of DMs below 500 pc cm⁻³, focusing on extragalactic sources to about 1 Gpc, and resulted in an upper limit of 1400 events per sky per day above a fluency of 6.0 kJy ms for an 8-ms pulse. Using a model for the distance-DM relationship, this equates to an upper limit of 134 events per Gpc³ per day.