Is there any truth to the claim that you should wait (at least) an hour after you wake up, before you start a workout. I've heard something about "the back is not lubricated enough before that" but that doesn't make sense in my opinion.
I haven't seen any scientific proof as to whether you should or shouldn't work out straight out of bed.
While you might be a little stiff at first, simply strolling for five minutes should be more than enough to get everything going. Sitting indoors for one hour won't nearly stress your body as much as just walking a little bit.
So as long as you start the workout a little relaxed, there's probably nothing bad that could happen to you. As for pulling a muscle or straining your back: listen to your body! If it starts complaining, slow down and take it easy, nobody said you should be pushing yourself and there's zero benefit to getting injured.
I agree with @Eelvex that making sure you drink something before you go (or taking something with you) is important, because you probably didn't drink anything for the past 6-8 hours. For the rest, your body will adjust itself quickly enough when you start walking.
I have no experience with weight lifting in the morning, but I reckon the same applies there: start with something light to get the blood flow going and increase the loads from there
According to StrongLifts.com, the theory behind not working out within the first hour of waking is actually the opposite to the one you mention - it's because the spine is too well hydrated and heavy compression (e.g. from weight lifting) or bending movements could cause a disk to rupture.
Bottom line is that you should never do any kind of exercise during the first hour after waking up. Here’s why: when you’re lying horizontally for hours, like when you’re sleeping, your back has no compressive loading. As a result, water fills back into your discs to nourish them. That’s the nightly hydration.
Now imagine your discs are water balloons. If they’re half full and you push one side, the water will move around and return when you let go. But if they’re full of water, they can burst when you push. Well this is exactly what can happen to your spine if you do any kind of heavy bending first thing in the morning.
The good news as Dr Stuart McGill explained in his book "Low Back Disorders" is that after the first hour of being up, your spine dehydrates by about 90% of what it will for that day (this is why you’re taller in the morning). So the risk of lower back injuries plummets after that first hour.
Apparently it takes about an hour or so for the fluid to drain out once you get up, hence the suggestion for waiting an hour before exercising. However a good warm up can supposedly help speed up this process. Dr Stuart McGill's claim does seem to be backed up by at least one study on PubMed.
Personally, I lift weights most mornings within about 45 mins of waking. I normally spend some time stretching my back on the foam roller first and always do a good warm-up (e.g. dynamic stretches or light weight versions of the exercises I will be performing). Obviously it's important to listen to your body and if something doesn't feel right then stop, but I haven't had any problems so far (and I actually broke my back a few years ago so I'm quite cautious). YMMV.
I have been working out in early morning (around 4.30 am) on empty stomach for past 6 months. I have yet to see negative effects on my body, but I have seen huge improvement in my strength, stamina and look.
I usually start with 20 minutes cardio which usually take care of everything (stiff body, hydration yada yada yada) and then I start hitting weights for about 45 min to an hour depending on body part I'm training. I drink a regular shaker bottle full of water and a 200mg caffeine pill right after I wake up and before I start getting ready for the gym.
Everybody has their different opinion about everything, what matters most is what is working out for you.