  We use heavy baryon chiral perturbation theory to evaluate the two-photon
exchange corrections to the low-energy elastic lepton-proton scattering at
next-to-leading order accuracy, i.e., ${\mathcal O}(\alpha, M^{-1})$, including
a non-zero lepton mass. We consider the elastic proton intermediate state in
the two-photon exchange together in the soft photon approximation. The infrared
singular contributions are projected out using dimensional regularization. The
resulting infrared singularity-free two-photon exchange contribution is in good
numerical agreement with existing predictions based on standard diagrammatic
soft photon approximation evaluations.
