A conceptual novel optics was developed for a future upgrade of the LHC interaction regions (IR). Applying the collision scheme with a large Piwinski angle and crab waist, originating from e+e- colliders, to an existing pp collider requires fairly unequal IP beta functions, while the transverse proton emittances are naturally equal. The extremely small vertical IP beta function calls for a novel final magnetic focusing element, a so-called double half quadrupole. At least a partial local chromatic correction is mandatory. Similar, simpler optics designs were explored for the LHeC electron beam. Possible benefits were also studied for higher-energy proton collisions at the HE-LHC, for which the proposed scheme appears quite attractive. Pertinent beam experiments were performed, analysed and prepared at DAFNE and LHC.