Local Care for Veterans Act - Directs the Secretary of Veterans Affairs (VA) to ensure that a veteran may elect to receive health care treatment and services under the Patient-Centered Community Care program if: (1) the veteran is enrolled in the VA health care system and resides not more than 50 miles from the nearest VA facility that the Secretary has identified in a prospectus level lease request as being deficient with respect to providing certain treatment or services or as needing expansion; and (2) the Secretary determines that such deficiency has not been resolved or such expansion has not occurred.