Lawrence, Kansas
Prior to Kansas Territory being established in May 1854, most of Douglas County was part of the Shawnee Indian Reservation (created in 1830). During this period, the Oregon Trail ran parallel to the Kansas River, roughly through the area where Lawrence would eventually be situated and a hill known then as "Hogback Ridge" (i.e., Mount Oread, which sits on the water divide separating the Kansas and Wakarusa River). This area was used as a landmark and an outlook by those on the trail. While this territory was technically unopened to settlement prior to 1854, there did exist a few "squatter settlements" in the area, especially just north of the Kansas River.
Oklahoma Panhandle
The Compromise of 1850 also established the eastern boundary of New Mexico Territory at the 103rd meridian, thus setting the western boundary of the strip. The Kansas-Nebraska Act of 1854 set the southern border of Kansas Territory as the 37th parallel. This became the northern boundary of "No Man's Land". When Kansas joined the Union in 1861, the western part of Kansas Territory was assigned to Colorado Territory, but did not change the boundary.