There is no search feature. For lives you can either press the LIVES button and scroll to the life you are looking for, or you can find where the life masters are located on the map (such as East Castele for miner) and click there to find them. It might take some getting used to but it generally shouldn't be too hard to find the quests you are looking for. Worst case scenario, you can click the ALL button and it'll show every quest. If you are looking for an obtained request from a life where there isn't a specific drop to pick up or monster to kill, you can click the location where their life master is and it'll show those quests as well, for example kill X amount of monsters with Y skill.
