Hey, that sounds very possible and like a very nice project. I think you should read up on the individual sensors and try them in a "stand-alone" mode. Once you have an understanding of how they work you can easily combine them to get a bike computer as you want it.
There are lots of tutorials online covering blinking lights and temperature/light sensors. The LCD-screen would be the most difficult part for me (I haven't work with that yet), but I think there are libraries availbale that makes it easy to use.
Good luck with that project!