Lyme Disease Initiative Act of 1998 - Directs the Secretary of Health and Human Services (acting through the Director of the Centers for Disease Control and Prevention and the Director of the National Institute of Health and the Secretary of Defense to collaborate in: (1) establishing specified public health goals relating to activities providing for a reduction in the incidence and prevalence of Lyme disease; and (2) carrying out activities toward achieving the goals directly or through grant awards or contracts to public or nonprofit private entities. Requires the Secretaries to establish a five-year plan for carrying out such activities and coordinating the programs and activities conducted or supported by the Government.

Lists as goals, in priority order: (1) developing a test to determine whether an individual has been bitten by a tick that has Lyme disease and a test for determining whether a patient has been cured; (2) reviewing the U.S. system for Lyme disease surveillance and reporting; (3) determining the average number of doctor visits before the disease is diagnosed; and (4) significantly increasing the number of physicians who have appropriate knowledge regarding the disease. (Sec. 4) Establishes the Lyme Disease Task Force to provide advice to the Secretaries on achieving the goals.

(Sec. 5) Requires the submission of annual reports by the Secretaries to the Congress until the goals are met.

(Sec. 7) Authorizes appropriations.

(Sec. 8) Expresses the sense of the Congress that the Food and Drug Administration should conduct a rapid and thorough review of new drug applications for drugs to immunize individuals against Lyme disease.