If the roof in the sunroom is also flat on the exterior part of the roof then perhaps put triangular windows in the top part of the wall that would look straight outside and then keep the sunroom ceiling flat. You wont notice its different as the window to the outside will be the feature of that wall.

The right side of the room is looking towards the ocean. I plan to have a fan in the middle and would like lights on each side of the fan but not down lights. I will explore your suggestions. Thank you

Hey there sonicamoya. not sure if you've made your decision yet, but have you considered halogen downlights with a dimmer? I also find floor lamps, like the one below, push light out and around, as opposed to just upwards. They are brilliant at adding light to a room: One last thing - consider adding some outdoor lighting, too. You could use outdoor fairy lights or solar garden lights. This will make the space feel less consumed with darkness, and encourage more flow between indoor and outdoor areas. Hope this helps :)

Just comes down to how much you're willing to spend. What some say is expensive maybe good with others. As oklouise said, have a chat with a builder. I'd have a chat with an engineer as well probably beforehand. Builder's can bump up estimation's if the project is unclear or looks difficult. Could be worthwhile having a chat with a designer (architect/building designer/etc) as they may be able to come up with a solution as well that can achieve a similar affect.