You both are really lucky then.
Let's say two people A and B, explains a situation (something bad) to C, and C tells them how lucky they are to escape from that bad situation. Now C responds, "You both are really lucky then."
What C is trying to say is that, as they escaped from a worse situation while many others didn't, they are lucky.
Now, is then at the end of the sentence grammatically correct or wrong? My doubt here is whether a sentence can end with then.
The word 'then' has many meanings. In some of its meanings, it is perfectly grammatical at the end of a sentence.
For instance, from definition 3.b from the Merriam-Webster online dictionary (here)
3.b: according to that : as may be inferred. 'your mind is made up, then?'
Another example is using this meaning (here):
1: At that time. 'Come at noon; I'll be ready then.'
The Macmillan dictionary describes the meaning of the OP's question directly:
3.b: As a result. (SPOKEN, used at the end of a question when you think something must be true because of what has just been said.)
"We went to the same school." "You're old friends then?"
You're not angry with me, then?
This last one was the meaning of 'then' in the OP's post.
Person C means "As a result of what you just told me, I conclude that 'you both are really lucky'."
"Then" in this context means "therefore." So the meaning of C's conclusion is, "You are both very lucky therefore.
