Greg would have none of the excuses. He was just about to tell him that he would not let him go home just like that, or more like take him home, since he wasn't in any kind of state to move around on his own, when the weight he held up with his arms grew heavier and Sherlock slumped over. Lestrade backed off a bit, taking a closer look. The detective was breathing deeply and regularly. So he had fallen asleep. ALso not something you saw from Sherlock everyday. Maybe all the yawning and the lack of words had been an indicator, but Greg, although he had noticed, had not thought that much of it. His thoughts had been rather hung up on the hospital thing. Which was one less problem to deal with now, it seemed. He just hoped Sherlock would stay asleep until he had no way to talk him into getting him home after all.
The ambulance arrived not too long afterwards, though it felt like much longer, because his amrs were getting heavy with trying to keep Sherlock upright and not make any of his injuries probably worse. Amazingly enough, the man slept through the whole ride and apparently even the examination. The man had to have been horribly wiped out.
Greg wasn't sure how long he waited in the area he had been shown to once they had arrived at the hospital, but he had made several calls to Donovan and worked, as far as he could since he wasn't leaving there, on the case. Once awake, he would make sure to occupy Sherlock buy telling him everything they had foudn out yet. That might actually be the only way to keep him from getting up and roaming about right away. 
Finally, after an hour or two, he was shown to a room, the nurse staying outside as he stepped in. He had been informed that besides the rather deep gash in his arm and a few cracked ribs, Sherlock had no too bad injuries. So he would be taking him home to Baker Street as soon as he was up and ready to go. But then he was still sleeping, so Lestrade sat down on the uncomfortable chair in the corner of the room and waited, writing in his notepad and texting with the people working on the case. He didn't take one call and put his phone on silent mode, Sherlock seemed to be needing this sleep badly.
Then he heard his name said and looked up. Greg smiled as he saw Sherlock looking around and got up walking over to the bed. "Slept well?" he asked teasingly, loking Sherlock over. To think all of this had turned out the way it had because of that one stupid bluff he had made. "You're fine, I was told. You have to be careful not to open that gash on your arm and a few of your ribs are a little cracked, so no fast movements or heavy carrying." he informed him. "If you're up to it, I can get you home now, as promised." he added, thinking he had seen something in the other mans eyes that made him offer it.