Use weapons which can hurt lycanthropes
In humanoid or hybrid form, lycanthropes can use weapons. If they are expecting to get into a fight with other lycanthropes, they would acquire weapons which can harm lycanthropes (in the same manner than non-lycanthropes would acquire weapons which can harm lycanthropes). Silvered or magical weapons are the obvious choices. Torches, since they deal fire damage, are good if proper weapons are not available.
Such weapons might be difficult to acquire and would be closely guarded by their owners, but if a fight with a lycanthrope is likely then it would be advantageous to have such weapons.
If any of the lycanthropes are spellcasters, they could attack their enemies with damaging spells. Magic weapon, if available, can allow a spellcaster's allies to also deal magic damage.
Poisons, if you can deliver them, can harm a lycanthrope. Injury poisons won't be much good unless you have a silvered or magical weapon, but inhalation or contact poisons are usable in combat and would work against lycanthropes. Ingested poisons would also work if you can manage to force-feed it to your target. However, poisons typically are rather expensive, so it may be hard to get enough for a full brawl.
Vials of acid or alchemist's fire are also options, albeit expensive ones.
Wrestle them into hazards (falling, suffocation, fire)
Falling deals bludgeoning damage but is not an attack, so lycanthropes take falling damage normally. To use this strategy, you need to either be able to fly or have a something at least 10 feet tall to push your enemies off.
Suffocation (PHB 183) can also kill lycanthropes. Forcing them underwater or strangling them would achieve that goal. In an evenly matched fight this strategy is unlikely to be viable, but if one side outnumbers the other (perhaps by picking off members one by one) then they could all work to restrain a target then either hold them underwater or choke them to death. The aggressor would need to hold this position for the full amount of time needed to drop the victim to zero hit points for it to have any effect.
There is no strict rules-as-written method for an arbitrary creature to cause another creature to choke. Bearing in mind that the rules of D&D 5e do not cover every possible action, strangling or choking would fall under Improvising an Action (PHB 193, sidebar). I'd point you to the Ettercap variant Web Garrote (MM 131) for a suggestion of one method to strangle a foe which can be easily adapted to a weapon which other creatures can use.
If you are uncomfortable with this kind of improvisation, it is still possible to drown an enemy by strict rules as written. Grapple an opponent then knock them prone in a body of water which is deep enough to immerse a prone lycanthrope but not a standing one. If the aggressor can securely restrain the victim, such as by tying them up, all the better. If the victim can be held there for a few minutes, they will drown.
Fire can hurt lycanthropes. While torches do a measly one fire damage, if you can shove a lycanthrope into a bonfire, or douse them in oil and set them alight, you would do a lot more damage.
It should be noted that, regarding traps which deal bludgeoning, piercing or slashing damage, some involve attack rolls (swinging blades and darts traps normally fall into this category), so would not harm a lycanthrope, while some do not require an attack roll (such as falling rocks or spiked pits or caltrops).