"Dice lost in combat are regained when the combat ends, at a "healing" rate determined by the GM."
Risus completely lacks a formal system of healing damage in combat. Instead, it is left to the discretion of the GM to determine when characters recover from damage (be it physical or otherwise). This can be unsettling to players who are used to games where such things are spelled out with absolute clarity (i.e. most other games). But after getting into the Zen of Risus, a GM will realize that this can be a powerful tool. Instead of relying on a fixed set of rules to restore combat capability to the player characters, the GM is free to use logic, common sense, and comedic/dramatic timing. There is no need for a "1 hour adventuring day" where wounded characters are forced to withdraw to a safe area shortly after breakfast. At the same time, the GM can make it painfully (or hilariously) difficult for characters to recover from a severe ass-whooping if it makes the game more fun.
Still, guideline are good. This is especially true for novice Risus GMs. The Risus Companion has about a page dedicated to useful advice about healing. There are also frequent discussions on this very topic on the RisustTalk mailing list. In my own games, I typically allow characters to make a "flesh wound" check after a fight to see if any dice can be recovered immediately. This "flesh wound" check is made using the current dice of a given cliche with every multiple of five on the roll restoring one die to the cliche. The "flesh wound" check is merely a guideline and I cheerfully toss it aside for damage described as obviously transitory (no roll required) or severe (it's going to take time and effort to recover).
Which brings us to the role of the healer...
In dungeon fantasy games, it is traditional that at least one member of the party function as a healer (i.e. cleric). His or her role is to enhance the capabilities of allies and restore them to fighting trim when they get whacked. The nature of the dungeon fantasy genre almost requires a healer, as the loss of resources (i.e. hit points) is typically designed into the adventure.
Though by no means required, a healer can be very useful in a Risus dungeon fantasy game. In fact, given that damage is not restricted to physical wounds, a healer who can restore cliches in short order becomes a viable concept in almost any genre. The presence of a healer will almost certainly affect the rate at which a good GM restores lost dice to characters. Players assuming healer roles are implicitly saying that they want to be stitching up wounds, counceling wounded egos, or repairing damaged hyperdrives. A good GM will provide ample opportunities for them to do so.
The most obvious place to do this is in the down-time after combat. This is almost always a Target Number roll (but see the Risus Companion for ideas on using combat for healing). The Target Number can be almost anything so consistency can be used to avoid the appearance of being arbitrary. Karl Paananen (in this RisusTalk post) suggests a Target Numbr of 5 times the number of lost cliches to heal a single cliche. I hadn't previously been using this particular formula but I like it will probably adopt it in the future (adjusted for the appropriateness of a cliche, of course).
There was also some discussion about healing/buffing allies during a combat. For my part, I say go for it. The healer would be giving up their own chance to attack that round and might expose themselves to attack on subsequent rounds. It prolongs the fight, but this is Risus - combats aren't terribly long anyway. Of course, healers can also fight as part of a team, with their contributed sixes being explained as the critical application of a Cure Light Wounds spell or ultra-tech stimpack.