There are unique and common adventures. Tombs, for example, will not regenerate unless you start a whole new save file, so those adventures can also not be regenerated. However, other "adventures", such as bring a gem to him, bring some nectar to her etc. type of missions, do regenerate, so it's perfectly possible to complete the LTW for several sims.
EDIT: Does anybody know what will happen with the "Great Explorer" LTW? My gut feeling from toying around with tomb markers in the buyDebug menu tells me that you just have to get the sim to the tomb chambers of 6 tombs in each destination, but can someone confirm or disconfirm?