Germany can send Lend-Lease to Vichy (Rule 14.4.3), but you cannot lend lease facilities, only IPP or Militaty units as was pointed out (Rule 7.9).
Furthermore, Vichy has no separate income since Germany receives income from all Vichy land zones (Rule 14.4.2 and Vichy QRS) and no build table, so its pointless to send IPPs.
Therefore, the only way that Vichy can get new units is through its Recruitement rolls or Lend Lease from Germany (and no other Axis power).