Attack Boost only increases your anti-personnel attack power; it does not affect damage against tanks.
Taken from a thread in the Steam Forum:
- Damage Boost order increases your vsArmor by 50.
- Demolition Boost order increases your vsArmor by 100.
For lancers, those bonuses are usually not very useful, since lancers deal multiple hundreds of damage to tanks from the beginning of the game (according to the VC wiki, the lances you start the game with already deal 850 damage vsArmor, minus the respective tank's defense value). As long as you have enough ammo, your lancers are better off attacking more often without these orders.
However, these orders can show great effect when used on Scouts, Engineers and especially Shocktroopers. I've had several games where I boosted Rosie with Demolition Boost and destroyed an enemy tank in a single move by going crazy on the tank's radiator with her machine gun (with every single shot being buffed by 100 vsArmor).
Another order to consider is the Penetration order, which lets you ignore the enemy's defense value. For your lancers, this should increase the damage dealt to tanks by a lot more than the Damage Boost or Demolition Boost would.