If one progresses in this lifetime, but doesn't attain enlightenment and doesn't become totally free from suffering, what can happen in future lives?
Nothing is lost. However a person below the level of Streamwinner is still subject to rebirth below the level of human being. The good kamma of having made an effort will eventually surface again and bring one back to a place where practice can be resumed.
The non-streamwinner is subject to stray and unskillful thoughts that can lead to a bad destination. Should such a tendency occur at the time of death, it's: 'Have a nice day!'
The principle is something like standing at the downtown platform in the subway. Up until the time one enters a car and the doors shut one can go over to the uptown platform, but once the door has shut on the downtown train one is going downtown at least for one stop.
This is the concern when it comes to attention to death, that is that one not be thinking, as the ordinary person thinks, that ok, death will come, but some time later. One should train to think that death is a possibility as close as a breath in and out or the chewing of a mouthful of food.
See for the above idea: http://obo.genaud.net/dhamma-vinaya/pts/an/06_sixes/an06.019.hare.pts.htm
and see for the practice:
This is why one should strive for Streamentry. At stream entry, the knowledge is firmly fixed that 'that which comes into existence comes to an end.' This idea at that point is so vivid as to present itself at the time of death and acts as a barrier to making a foolish decision at that time, and the ball has been set rolling for an inevitable attainment of Arahantship within a period of no more than seven further rebirths in various heavenly states and among men.