Am I required to file a Kentucky Tax return when my only income in the state is under $100 (proceeds from an Oil and Gas lease)? I am not a resident of KY.

According to "2019 Kentucky Income Tax Return Nonresident or Part-Year Resident", 740-NP, Form 740-NP must be used by full-year nonresidents who had income from Kentucky sources and by part-year residents who had income while a Kentucky resident or from Kentucky sources while a nonresident. These persons must file Form 740-NP if (1) they had any gross income from Kentucky sources and gross income from all sources in excess of modified gross income for their family size, or (2) Kentucky gross receipts from self-employment in excess of modified gross income for their family size. See Chart A on page 10.

On Page 10:

Modified Gross Income—Modified gross income is the greater of federal adjusted gross income adjusted to include interest income derived from municipal bonds (non-Kentucky) and lump-sum pension distributions not included in federal adjusted gross income; or Kentucky adjusted gross income adjusted to include lump-sum pension distributions not included in federal adjusted gross income.
Chart A
Your Modified Gross
If Your Family Size is: Income is greater than:
One............................. and ............................ $ 12,490
Two ............................ and ............................ $ 16,910
Three.......................... and ............................ $21,330
Four or More ............. and ............................ $ 25,750

https://revenue.ky.gov/Forms/740-NP%20Instructions%20Packet.pdf