The Large Hadron-Electron Collider (LHeC) will operate at $sqrt{s}$ = 1.2 TeV and accumulate about 1/ab of integrated electron-proton luminosity. Novel studies of high energy photon-photon interactions at the LHeC, at the $gammagamma$ center-of-mass energy up to 1 TeV, will open new frontiers in the electroweak physics as well as in searches for physics beyond the Standard Model. Despite a very high $ep$ luminosity, the experimental conditions will be very favorable at the LHeC - a negligible event pileup will allow for unique studies of a number of processes involving the exclusive production via photon-photon fusion.