Should I acept my second choice? I applied to a PhD program, and after all the interviews I got a firm offer for a fellowship let's call it PhD A, that I have to give an answer to before a deadline (next week), since they have
Now the lab in which I did my master's thesis, and in which I have been working since 6 months applied for a grant to finance a PhD student (me) but won't have an answer before a May. Let's call this PhD B.  

Now my problem is that I would prefer staying in the lab I am at for PhD B, but, even though it might be small, there is always a chance that it wont get the grant, so if I say no to PhD A I would be left with nothing.
And on the other hand, if I accept the fellowship offer for PhD A and my lab gets the grant, I would prefer doing PhD B.

The real problem is this deadline, because the PhD A wouldn't start before October, and so if I also get an offer for PhD B after having accepted offer A, I would prefer not to burn any bridges by just leaving after having accepted.  

So my question is what do you think can be done in a situation like this?
In this case, I would do the following first. Go to your present admin/PI and let them know what you have said here and ask them what would happen if they don't get the grant. Is there the possibility that you can be kept on with other funding, or is it absolutely dependent on the grant? 

If you are valued enough where you are, it is just possible that they can make some arrangement to keep you. "I'd rather stay, but it seems uncertain, and I have this other offer. What can be done?" 

I think it is probably worth asking the question. 

But if it isn't possible to make an accommodation, then you need to decide how much risk you are willing to accept. That is personal. It would depend on the likelihood of other options, of course.