LnD works with Blade tome?

No. Buffs added to bladetomes are buffs gained from the following skills: Hone, Fortify, Rally, Tactic, Defiant (hopefully I didn’t miss any). Basically, any buffs that make your stats turn blue when you’re on the map.

Life and Death doesn't count towards Bladetome's damage because it's not a visible buff, it just adds the numbers to your stats like you're equipping a weapon. Only things like Hone, Fortify, PA!Azura's Uror, FlyZura's Earth Dance (I think that's the name of it), PA!Inigo's Gale Dance, etc. They give visible buffs (blue numbers during combat).