Episodic accretion in protostars leads to luminosity outbursts that end up heating their surroundings. This rise in temperature pushes the snow lines back, enabling the desorption of chemical species from dust grain surfaces, which may significantly alter the chemical history of the accreting envelope. However, a limited number of extensive chemical surveys of eruptive young stars have been performed thus far. In the present study, we carry out a large spectral survey of the binary Class I protostar L1551 IRS 5, known to be a FUor-like object, in the 3mm and 2mm bands with the IRAM-30m telescope. As a result, we detected more than 400 molecular lines. The source displays a great chemical richness with the detection of 75 species, including isotopologues. Among these species, there are 13 hydrocarbons, 25 N-bearing species, 30 O-bearing species, 15 S-bearing species, 12 deuterated molecules, and a total of 10 complex organic molecules (l-C_4_H_2_, CH_3_CCH, CH_2_DCCH, CH_3_CHO, CH_3_CN, CH_3_OCH_3_ , CH_3_OCHO, CH_3_OH, CH_2_DOH, and HC_5_N). With the help of local thermodynamic equilibrium (LTE) and non-LTE models, we determined the column densities of most molecules as well as excitation and kinetic temperatures. While most of those molecules trace the cold envelope (<20K), the OCS and CH3OH emission arise from the warm (>100K) innermost (<2arcsec) regions. We compared the chemical inventory of L1551 IRS 5 and its column density ratios, including isotopic ratios, with other protostellar sources. A broad chemical diversity is seen among Class I objects. More observations with both single-dish telescopes and interferometers are needed to characterize the diversity in a larger sample of protostars, while more astrochemical models would help explain this diversity, in addition to the impact of luminosity outbursts on the chemistry of protostellar envelopes.