In by the book LotFP, only fighters get an increasing attack bonus. While this is appropriate for some games, others may wish to grant non-fighter classes some greater degree of combat effectiveness.
Gus L. suggested on G+ that maybe specialists could gain an increasing bonus to missile attacks and that clerics could gain an increasing bonus to melee attacks. I like that division, and it inspired the slightly more nuanced structure below.
- Cleric: as fighter against unholy foes (undead, demons, etc)
- Dwarf: as fighter, but only for melee attacks
- Elf: as fighter but only with elven weapons (see * below)
- Fighter: unchanged (increasing attack bonus for everything)
- Halfling: as fighter for small thrown missiles
- Magic-user: unchanged (no increasing attack bonus)
- Specialist: +1 melee or missile attack each level (pick), trap-making (see ** below)
Each of these rules alludes to mythological or thematic inspirations for the class in question. The halfing, for example, is reminiscent of David and Goliath. The specialist rule plays on the idea of discretionary focus (this allows you to make, for example, a thug specialist that is just as competent as a fighter, but only in melee). And so forth. They are also less boring than the more common approach of just giving smaller bonuses to the non-fighter classes (most commonly, I have seen +1 every other level proposed for the semi-martial classes). They also stay within the niche design of LotFP, allowing most classes to be competent combatants, but only in specific ways.
* Elven weapons. This goes to the otherworldly nature of elves (and also, perhaps, their comedy value if you want to play up the snobbishness aspect). Exactly how you operationalize what it means to be an elf weapon will drastically affect the power of this rule. I would suggest not iron and not steel are clear criteria, and probably quality. For a simple rule of thumb, you could make elven weapons cost ten times as much and only be available in Elven strongholds.
** Trap-making. This allows specialists to create makeshift traps given basic supplies and a turn of prep time. The trap attacks as a fighter of the specialist’s level (or in the context of the above discussion, the specialist’s attack bonus is that of a fighter when expressed in prepared traps).