We present new broad-band X-ray observations of the z ∼ 2.5 lensed quasar 2MASS J1042+1641, combining XMM–Newton, Chandra, and NuSTAR to provide coverage of the X-ray spectrum over the 0.3–40 keV bandpass in the observed frame, corresponding to the ∼1–140 keV band in the rest frame of 2MASS J1042+1641. The X-ray data show clear evidence for strong (but still Compton-thin) X-ray absorption, NH ∼ 3–4 × 1023 cm−2cm−2, in addition to significant reprocessing by Compton-thick material that must lie away from our line of sight to the central X-ray source. We test two different interpretations for the latter: first that the reprocessing occurs in a classic active galactic nucleus torus, as invoked in unification models, and second that the reprocessing occurs in the accretion disc. Both models can successfully reproduce the observed spectra, and both imply that the source is viewed at moderately low inclinations (i < 50°) despite the heavy line-of-sight absorption. Combining the X-ray data with infrared (IR) data from WISE, the results seen from 2MASS J1042+1641 further support the recent suggestion that large X-ray and IR surveys may together be able to identify good lensed quasar candidates in advance of detailed imaging studies.