The present invention provides a high pressure discharge lamp with a start-up assist member, a lamp unit, and a lamp system that reduce breakdown voltage and provide high design flexibility by reducing restriction on a position of an adjacent conductor. In a high pressure discharge lamp (10) of a lamp unit (1), a dielectric member (20) is on the outer surface of a first sealing part (101a). The dielectric member (20) made of a titanium compound has relative permittivity higher than that of fused quartz. An upstream end of a metal wire (21) is connected to an external lead wire (102b) projecting from a second sealing part (101b). A downstream end (21A) is in contact with the dielectric member (20). Upon lighting of the lamp, a corona discharge occurs at the point where the end (21a) is in contact with the dielectric member (20) so that breakdown voltage is reduced.