The invention relates to an intermediate case for a twin spool turbomachine for an aircraft, comprising at least one lubricant passage and piece (88a) associated with at least one of its vanes (24), comprising a lubricant passage (98a) extending along a passage axis (134a) and opening up into the lubricant duct (55a). The passage axis (134a) and the orifice axis (140a) are also at a spacing from each other along a circumferential direction (91), and a connection piece (125a) through which a connection conduit (142a) passes is firstly partially housed in the vane root (34) so as to create a communication between the connection duct (142a) and the lubricant passage orifice (124a), and secondly is partially housed in an end-piece support device (108a) or in the lubricant passage end-piece (88a), such that the connection conduit (142a) communicates with the lubricant passage (98a) in the end-piece.