Well, nobody gives you 100% guarantee that everything will work update update, that is why there is a warning there. As per my experience, Easy Apache is pretty stable and if it fails to compile something it simply leaves the old version of softwares running. So, if you are sure that you scripts are compatible with PHP 5.3, I would give it a try. If something happens that stops your site from the resolving, just call dedicated support to get immediate assistance.
Additionally, if you have managed intense addon purchased with your plan, Lunarpages admins can do the update for free for you. Otherwise, there will be custom configuration free of 60$ for each 30mins of work. EasyApache shouldn't take more than 30 mins, unless something wrong happens.
Finally, I would like to mention that dedicated customers have priority support on the desks and there should be no tickets waiting for days of reply to them.
Please advise, if you have any adidtional questions.