The RFOFO ring and its derivative Guggenheim helix are the two efficient lattices for the initial stage of cooling in the Muon Collider. However, they have a certain disadvantage, namely, the RF cavities operate in a strong magnetic field. R\&D results to date suggest that this may cause breakdown of cavities before reaching desired RF gradients. The open cavity lattice studied in detail in this article attempts to address this problem by moving the magnetic coils into the irises of the RF cavities and shaping the cavities in such a way that the magnetic field lines are parallel to the walls. In such a layout the electrons do not gain enough energy to damage the walls, thus allowing the design gradients to be reached.