You are not committed to worth with either lender at this point in time, all work completed to date should be preliminary and not have cost you anything, although I do not recommend flipflopping lenders. You should choose a lender and work towards closing period... flipflopping will cause unnecessary delays, and complications, compromising terms and frustrating everyone involved including yourself. It is a prescription for misinformation as the two lenders will most likely quote different rates and costs which you could argue over until the sun turns blue. Point in fact, if your rate is not locked by either lender, what they are quoting at the particular time is irrelevant - the terms will change as the market moves so why waste the energy arguing over spilt milk.
What you need is a lender that you can trust. Do you trust - I mean TRUST - either of these lenders? If the answer is no for both of them, I suggest cancelling with both and finding a lender that you can and do trust. If you do trust on of these lenders, that is who you should be working with. Let them know they are your choice for closing, and when you expect the loan to close. If they have a problem meeting this closing date they should let you know. Lock your interest rate based on this closing date. If the rate you want is available at the terms you are comfortable with currently. Lock, it's too volatile to risk at this point in time.
As for waiting on your approval. Turntimes are not very long right now so you should not have to wait very long, and you should not have to wait for the approval to lock the rate. This type of action speaks towards the lenders confidence in the loan closing. If they are confident you will qualify, know the guidelines and what will be conditioned, and trust you are not going to walk away from them; your lender can and will lock the loan for you. They have not locked yet because if they do not deliver a locked loan, it hurts their performance rating and can jeopardize their approval status. This is not a good enough reason for you to stay with them especially if the terms you want can be locked in now.
My advise is get the loan locked with the lender you plan on closing with. Stop working with the other and focus all your attention on the one lender. Talk to both lenders right now and tell them you want to lock and ask what their pricing is, whoever has the best pricing is who you move forward with.
Best of luck.