Countering Hezbollah in Lebanon's Military Act of 2019 This bill limits the use of security assistance funds for Lebanon until certain conditions are met. Specifically, 20% of funds appropriated or made available for such security assistance may not be obligated or expended until the President certifies to Congress that (1) the Lebanese Armed Forces have taken measurable steps to limit or expel Hezbollah-influenced military personnel that have significant influence over the Lebanese Armed Forces' policies or activities, (2) activities of the Lebanese Armed Forces to disarm Hezbollah demonstrate a serious commitment to fulfill United Nations Security Council Resolution 1701 calling for such disarmament, and (3) the Lebanese Armed Forces have not cooperated or partnered with Hezbollah during the last year. The President may waive the first two requirements if it is in U.S. national security interest to do so.