I've been pretty disappointed with the Monk Class in the past. It's often a half-assed thief with super fighty powers bolted on top. The beauty of the LotFP system is the point system for skills is more flexible than the percentages for thief skills so there is no reason to feel bound by any of that stuff. The Lamentations adventure Qelong has the Lotus Monk but it's for NPCs only and is basically a mystical fighter with magic powers. It is not a great fit to make a player character in the old west.
LotFP has a system in place to avoid power creep and protect the Fighter's place amongst the classes. The only class that increases in attack bonus is the Fighter, all the others have the +1 attack bonus they start with. I don't think the Monk Class needs an attack bonus to still have the flavour of a mystic/unstoppable warrior.
Monks are incredible athletes, performing amazing feats of balance and withstanding terrible punishment that would drop lesser people. Taking that into account, the best LotFP class to use as the base for the Monk is the Dwarf. The Monk would use the Dwarf experience table and saving throws. The Architecture Skill would be replaced by both Climb and Stealth. None of the other Dwarf abilities would apply and the Monk would use the D8 hit die of the Fighter and use the Fighter minimum hit points for first level to represent their physical resilience. At tenth level the Monk uses a +3 and no constitution modifier instead of additional hit dice.
(The Climb skill for the Monk Class)
Climb is not the careful scaling of sheer walls the Specialist would do but more of a leaping, acrobatic bouncing from surface to surface to ascend bare walls. Stealth is an obvious choice for a monk.
Despite the obvious vitality of monks the Constitution modifier the Dwarf gets is not entirely appropriate. Much of the monk's abilities come from a greater connection to the world and their training is centred around that. The Monk Class gets a +1 Wisdom Modifier.
To embrace the mystical aspect of the monk, add the total wisdom modifier to Open Doors rolls to show how their connection to the world around them gives them power over it and allows them to punch through doors and whatnot. The Referee can apply any necessary modifiers for different materials but I would likely let the Monk PCs break harder and harder materials as they level up.
The monk in Qelong adds level to AC, attack bonus and so on. With this setup, the Qelong monk becomes absolutely ridiculous around level 8. The LotFP Rules are designed to avoid power creep so I think the standard +1 attack bonus is sufficient and no AC improvement ladder is necessary.
I like the monk as a fast, difficult to hit character in tune with the space surrounding him or her and able to use that connection to the world to fight with a preternatural speed.
Wisdom is a huge factor in the Monk's ability to attack and defend. When not wearing armour the monk adds the total wisdom modifier to Armour Class. This bonus is usable with a shield, while making use of cover and in addition to any modifier from dexterity. As long as the monk is only lightly encumbered s/he adds wisdom to his/her attack bonus in addition to any other modifier. These combinations make the monk pretty bad-ass out of the gates at first level, but if you are using the normal roll-three-in-order character generation it should not imbalance the game.
Monks are experts at evasion and grappling. When wrestling they add their level to the D20 roll instead of their attack bonus. A monk may also substitute the wisdom modifier for the strength modifier. Monks can use either wisdom or strength when wrestling, not both. You can fight smart or strong, but not both at once.
Monks are renowned for their ability to fight with and without weapons. The precision and speed of their strikes defy reason. To represent the flurry of of strikes landing in a single round and the improvement that only experience can bring, the Monk's hand-to-hand damage is determined by level rather than the weapon used. This starts at 1D4 at first level. It increases to 1D6 at second level. At fifth level it increases to 1D8. It increases to 1D10 at eighth level and finally to 1D12 at tenth level.
As a warrior of exceptional training, like the fighter, the monk can use the martial manoeuvres: Press and Defensive Fighting.
That sums it up. A simple version of the monk with a framework of rules that should allow a player to roll to do cool monk-like stuff without making and of the other classes redundant. The focus on the physical suits a more modern setting and will work well with the Weird Old West.