Lincoln General Hospital covered a large area around Lincoln Park during the Civil War. Since President Lincoln was known to visit many hospitals during the war, it is possible that he visited this hospital some time during the war.
The following image and information is comes from the US National Library of Medicine at http://www.nlm.nih.gov/hmd/medtour/lincoln.html
Lincoln General Hospital
East Capitol and 15th Streets
Opened in December 1862, Lincoln General was the largest of the military hospitals in the area built by the Army to take care of the Civil War casualties. It was located on Capitol Hill, 15 blocks east of the Capitol building. The hospital complex included 20 pavilions, arranged in two lines forming a V, and 25 tent wards, which provided altogether a bed capacity of 2,575. The kitchen and dining rooms were connected to the pavilions by means of a covered pathway. In addition to the headquarters (marked by the flag), there were officers quarters, quarters for Sisters who provided nursing service, barracks, guard house, separate quarters for contrabands, and service facilities such as water tank, laundry, barber shop, carpenter shop, stables and a morgue ("Dead House"). Like most other military hospitals, Lincoln General was taken down shortly after the Civil War. The area once occupied by Lincoln General is now a residental district.