(it help if you link or quote what you're asking about)
"Diseased: The paladin's lay on hands ability also acts as remove disease, using the paladin's level as the caster level."
"Bracers of the Merciful Knight
Source Ultimate Equipment pg. 272
Aura moderate conjuration; CL 9th
Slot wrist; Price 15,600 gp; Weight 1 lb.
Description
These golden bracers are engraved with images of celestial creatures. When worn by a paladin, he is considered four levels higher for the purposes of determining the uses per day and healing provided by his lay on hands class feature. Additionally, once per day, the wearer can infuse a use of lay on hands with additional power, providing relief as a lesser restoration spell."
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So strict RAW when the item talk about healing done by the lay on hands it mean the hp healing. disease are cured or removed not healed. that mean that RAW answer is a no.
-but i can see a lot of GMs (including me) who would allow for anything that ride on the lay on hands to also get the same level up.
truth be told a lot of GM do not like the players to stay diseased (unless it's for roleplay, aka vamp\lycen stories), they tend to be grumpy about it and GM rather the players to enjoy the game.
you are using a 15k+ worth of an item and a lay on hands to try and remove the disease? i'd let you get that +4 to caster level check the item give for the healing of hp to the removal of the disease check.
it's still only a chance to remove the disease AND the item is named after the mercy ability not he lay on hands ability, it should have some effect on the mercies used with it.
I would counter with a lot of GMs also don't like mechanics to be trivialized and plenty of enemies, traps, and scenarios have disease as part of their mechanic. Considering that every use of the lay on hands is an attempt to remove the disease, it really doesn't need a +4 for something you can already do 6-8 times per day (at level 8), 2 more times already with the bracers, when the effects of the disease are only once per day anyway.