The short answer is no, it is absolutely not normal for an adult do to lose teeth.
Dogs, like people, lose their deciduous (baby) teeth before adulthood. Most deciduous teeth fall out by 7-9 months of age.
From your description I suspect that Mikka lost an incisor tooth. These are small teeth found in the front of the mouth, top and bottom. They are used to grasp things (food, toys). This is a link to a picture of a dog's upper 6 incisor teeth: https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQEj-rcxtM9W2-yl26WJdbH637tR5Ui-fSqTENv0No72ybbFMQYjw
They have fairly long roots, and most of the time if they fall out a section of root is left behind in the jaw. I suspect that may be why she keeps licking the area.
Here is a link of a radiograph of a dog's lower jaw showing how long normal incisor roots are: http://www.thepetdentist.com/300/6%20x-ray%20showing%20infection%20around%20root%20tip%20of%20left%20lower%20canine%20tooth.jpg
They can be broken by overzealous play, especially tug of war play. Or the roots can become loosened by overcrowding and/or a collection of tartar and secondary gum damage.
I know that dental care is expensive, but if there is a root fragment that is painful for your pup and predisposes to developing a jaw infection. If your regular veterinarian is beyond your means financially now your other option is to contact your local shelter or humane society and see if they run a low cost clinic or know of one in your area.
If not here is a web-page that lists some that may be able to help:
Other sources of help can be found here: http://speakingforspot.com/?p=Financial%20Assistance%20for%20Veterinary%20Care
Your girl really needs veterinary care. Oral infections often spread via the bloodstream to other organs and can lead to chronic systemic infections.
Please let me know if you have any further questions.