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You don't need particularly formal wear on Louis Cruise Lines. However, like on virtually all lines, a certain standard is required, i.e. no shorts for dinner etc.
For the formal nights, a jacket and tie for gentlemen and a corresponding dress for ladies is adequate.
As for more upscale lines that offer casual cruises (Louis actually is a budget line), Oceania Cruises is my recommendation if you are looking for mid-sized ships, superb cuisine and service as well as for a casual atmosphere with no formal nights. Newcomer Azamara Cruises is more or less an Oceania clone (even using the same class of ships), but it remains to be seen whether that cruise line will be able to deliver the same high standard. Personally, I haven't tried Azamara, yet.