It's to big a topic to discuss in depth here, and I don't want to use my lighting design program to give you an answer (as I think this is a homework question and I would need much more information such as working plane, surface reflectance, light pattern polar diagram, etc). It isn't a simple "oh that will give you x lux" answer.
Try these links for detailed information on illumination engineering and how to perform the design.
If you want anything more than a rough estimate you are going to need an illumination engineering design program. There should be a few free ones on the internet (Stahl have one) but you need to know the basics on illumination engineering first as illumination is a bit of a "black art".
You are going to need to look as many of the programs are not free and others are limited time demos (in which case you need to know the basics of illumination engineering to allow you to learn and use the program fast). also try adding freeware or shareware or free into the search string.
I would stick with a free one you can try out over a period of time and learn from.
Let us know if you find a functional one that is easy to use so we can recommend it to other interested students and semi-professionals.