The City of Lynchburg is the biggest city in Virginia without direct access to an interstate highway. The nearest interstate to the city is I-81, which is over 20 miles from where US 501 enters the western city limits.
History:
The first freeway built in Lynchburg was the Lynchburg Expressway, which was built as US 29 before 1955. That year, the freeway was only completed from the James River to Kemper Street. By 1959, the Lynchburg Expressway was extended south to Wards Road and north into Amherst County.
Between 1962 and 1968, the freeway was extended even further south to Timberlake Road/Fort Avenue. In 1975, the Jerry Falwell Parkway was opened between the Lynchburg Expressway and US 501 (Campbell Avenue). By 1978, the Lynchburg Expressway was extended to Forest Road and signed as VA-291.
The Jerry Falwell Parkway was extended south to Wards Road with the VA-224 designation by 1982, and around 1989, the freeway was completed and VA-224 became part of US 460. In 1990, the rest of the Lynchburg Expressway was built and VA-291 was renumbered as part of US 501.
In 2004, a new freeway was opened, which ran from VA-210 in Amherst County south to US 460 at the northeast corner of Lynchburg. The freeway got the Monacan Parkway name before getting extended north to Amherst the next year and becoming part of US 29.
Lack of Interstates:
Lynchburg obviously has no interstates, though there is an alternate timeline where the city has I-64 and I-85 running through/near it.
Likely the main reason I-85 doesn't go anywhere near Lynchburg is due to the hilly terrain it would have to follow from Danville, to Lynchburg and possibly even Charlottesville. Instead, US 29 is a 4-lane divided highway north and south of Lynchburg, while being a freeway in and just north of the city.
I-64 could also be going through the city too. When the interstates in Virginia were being planned, the CTB planned for the interstate to head south from Clifton Forge, having an interchange with I-81 north of Roanoke, then following US 460 into the Lynchburg area and east, before using US 360 towards Richmond.
This routing was overturned by the federal government in favor of a northern route continuing east from Clifton Forge towards Lexington, using I-81 to Staunton and following US 250 through Waynesboro, Charlottesville and eventually Richmond.