What does that mean?!? Lineal?
In a perfect world, it means nothing, as there would never be a reason for a champion to "lose" his belt outside of a title fight. The lineal title exists when that situation does happen, when champions lose in a non-title fight (catchweight, someone missing weight, fight outside that promotion) or having their title stripped for one reason or another (failed drug test, retirement, significant injury/recovery, leaving the promotion)
For example, the path of the UFC HW lineal title;
-Mark Coleman (def Dan Severn, UFC 12)
-Maurice Smith (UFC 14)
-Randy Couture (UFC Japan, stripped of official title after contract dispute, vacant title awarded to Bas Rutten after defeating Kevin Randleman)
-Enson Inoue (Vale Tudo Japan 1998)
-Mark Kerr (Pride GP 2000 Opening Round)
-Kazuyuki Fujita (Pride GP 2000 Finals)
-Mark Coleman (Pride GP 2000 Finals)
-Antonio Rodrigo Nogueira (Pride 16)
-Fedor Emelianenko (Pride 25)
-Fabricio Werdum (Strikeforce: Fedor vs Werdum)
-Alistair Overeem (Strikeforce: Overeem vs Werdum)
So, Overeem is the reigning Dream HW Champion, Strikeforce HW Champion (Cormier was only the HWGP Champ), 2010 K-1 HW Champ AND the lineal UFC and Pride (having passed from Fedor to Werdum to Overeem) HW Champion.
Interestingly Cung Le is still the Strikeforce Lineal MW champion (having lost it to, then reclaimed it from Scott Smith, losing it to Wanderlei Silva, who lost it to Rich Franklin, who then lost it to Cung Le).
GSP holds the second strain of the Strikeforce MW title (having defeated Jake Shields, who won the vacant belt defeating Mayhem Miller after Cung semi-retired) AND the WW title (defeating Carlos Condit who defeated Nick Diaz).