Found old friend on Facebook. Sent message. Message accepted. Facebook says 'you and so & so are not connected on Facebook'. How do we send a friend request?
I think your friend has a privacy setting for Who can send friend requests?. If your friend has set it as Friends of friends and you both do not have any mutual friends, you will not see Add friend button or if your friend has set it No One, in that case Add Friend button will not visible on his/her profile.
Another case is may be your friend already has friends to the limit (5000). In this case he/she will not be able to add more people as a friend.
People can select the audience they want to receive friend requests from in their settings. You might consider sending your friend a message and asking them to friend you.
To know about friend requests privacy see this Help Center article.