I am very new to cloud computing. I was wondering can i develop a website using LAMP stack on cloud.
And which cloud to use. Is there any open source cloud out there to use it.
Sort of. You can use Eucalyptus to develop applications that would run on Amazon's EC2 using the LAMP stack. Eucalyptus is open source. Everything you run on an EC2 instance can be open source, but the actual EC2 instance is paid for (if that's what you were trying to avoid).
EC2 is cloud computing in the Hardware-as-a-service sense.
You can use Java or Python (and soon Go) to develop applications on Google AppEngine, but you don't even see the operating system and the application container is not really applicable. So that kills the LA portion of LAMP. Also, AppEngine uses various DataStore API hooks, so the M isn't really applicable. So as long as the P was Python and not PHP, you're golden (again, assuming P is a reasonable substitute for LAMP). On the plus side, you can do quite a bit before hitting the AppEngine quotas and having to pay for anything. Note that you can get an open source AppEngine work-alike with appscale. As a bonus, appscale runs on Eucalyptus (this might have something to do with the fact that the creators of appscale and eucalyptus are married).
Heroku is good for deploying Rails applications, but that's not exactly LAMP, either.
Heroku and AppEngine are cloud computing in the Platform-as-a-service sense.
(hopefully you get other answers)