Frogbyte- Bill Hartman has a good blog post from a while ago on this exact issue. Training in the morning is certainly more risky but can still be done safely. Rounding your lower back when getting dressed and driving to work is just as, if not more risky than training in the morning.
http://billhartman.net/blog/2008/01/21/ ... sc-injury/
fast_twitch - I would advise you make it a priority to learn a little about the lower back. I don't mean to get a degree in biomechanics, just learn enough to manage it properly. For example, hyperextensions and supermans are things you should be avoiding. The series of articles that frogbyte linked to are a great source of info.
In a nutshell, you want to avoid any excess movement at the lower back. The movment should come from the upper back (i.e. the chest) and hips. The upper back has the capacity to move around a lot, the lower back doesn't. Specifically, you want to stay away from anything that rounds your lower back. So, if the your back rounds and the rounding is taking place from your hips to around your belly button, then you're rounding the lower back - you want to avoid that. For pretty much the same reasons, you want to avoid bending backwards excessively i.e. hyperextensions. The 'extension' part is fine (if it's pain free), it's the 'hyper' part that's the problem. Supermans put your lower back in the same position. Traditional Sit ups/crunches round your lower back - it's these kind of things you need to become aware of, really.
As for training in the morning - you should read the blog post above. Of course you can train in the morning, you just need to be extra catious. I would advise you to train at night or the afternoon if you have the option, but, if the morning is the only time you can train, then just train, but be careful/sensible.
Also, the morning is actually a good time for people with back issues to get moving as it will generally make it much more managable, much quicker. Bodyweight squat, lunge, and plank type movements would be good to loosen you up and, done properly, should easily keep you out of the 'danger zone' (rounding, or bending back excessively). So, if you stop training in the morning, you might want to do a short (5-10) minute body weight routine, nice and easy going, just to help things a long.
Also - golden rule is, if it hurts, don't do it.