We present spectroscopic observations in the rest-frame optical and near- to mid-infrared wavelengths of four gravitationally lensed infrared (IR) luminous star-forming galaxies at redshift 1 <z < 3 from the LUCIFER instrument on the Large Binocular Telescope and the Infrared Spectrograph on Spitzer. The sample was selected to represent pure, actively star-forming systems, absent of active galactic nuclei. The large lensing magnifications result in high signal-to-noise spectra that can probe faint IR recombination lines, including Paα and Brα at high redshifts. The sample was augmented by three lensed galaxies with similar suites of unpublished data and observations from the literature, resulting in the final sample of seven galaxies. We use the IR recombination lines in conjunction with Hα observations to probe the extinction, Av, of these systems, as well as testing star formation rate (SFR) indicators against the SFR measured by fitting spectral energy distributions to far-IR photometry. Our galaxies occupy a range of Av from ~0 to 5.9 mag, larger than previously known for a similar range of IR luminosities at these redshifts. Thus, estimates of SFR even at z ~ 2 must take careful count of extinction in the most IR luminous galaxies. We also measure extinction by comparing SFR estimates from optical emission lines with those from far-IR measurements. The comparison of results from these two independent methods indicates a large variety of dust distribution scenarios at 1 < z < 3. Without correcting for dust extinction, the Hα SFR indicator underestimates the SFR; the size of the necessary correction depends on the IR luminosity and dust distribution scenario. Individual SFR estimates based on the 6.2 μm polycyclic aromatic hydrocarbon emission line luminosity do not show a systematic discrepancy with extinction, although a considerable, ~ 0.2 dex, scatter is observed.