We present the detection at 89 μm (observed frame) of the Herschel-selected gravitationally lensed starburst galaxy HATLAS J1429-0028 (also known as G15v2.19) in 15 minutes with the High-resolution Airborne Wideband Camera-plus (HAWC+) onboard the Stratospheric Observatory for Infrared Astronomy (SOFIA). The spectacular lensing system consists of an edge-on foreground disk galaxy at z = 0.22 and a nearly complete Einstein ring of an intrinsic ultra-luminous infrared (IR) galaxy at z = 1.03. Is this high IR luminosity powered by pure star formation (SF) or also an active galactic nucleus (AGN)? Previous nebular line diagnostics indicate that it is star formation dominated. We perform a 27-band multiwavelength spectral energy distribution (SED) modeling including the new SOFIA/HAWC+ data to constrain the fractional AGN contribution to the total IR luminosity. The AGN fraction in the IR turns out to be negligible. In addition, J1429-0028 serves as a testbed for comparing SED results from different models/templates and SED codes (MAGPHYS, SED3FIT, and CIGALE). We stress that star formation history is the dominant source of uncertainty in the derived stellar mass (as high as a factor of ∼10) even in the case of extensive photometric coverage. Furthermore, the detection of a source at z ∼ 1 with SOFIA/HAWC+ demonstrates the potential of utilizing this facility for distant galaxy studies including the decomposition of SF/AGN components, which cannot be accomplished with other current facilities.