To lack something is to simply not have that thing; to be deprived of something is to have suffered the loss of that thing. For example, as a human being, I naturally lack wings. I have not been deprived of wings, since wings are not part of human nature. Conversely, a bird lacks arms, but is not deprived of them, because arms are not part of avian nature. If I had been born without arms, I would have been deprived of them by a birth defect, for they are part of human nature, just as a bird born without wings would be deprived of and not merely lack wings.
When God created man, he could have created him in what is called the state of pure nature, in which he did not have the supernatural endowment of sanctifying grace. Had the human race persisted in that state, children would be born lacking sanctifying grace, but not deprived of it. Instead, God chose to create man in what is called the state of elevated nature, in which our first parents were endowed with sanctifying grace as a gift not just to them but to their posterity. Unfortunately, they lost this gift for themselves and for us, and so now we are born deprived of sanctifying grace. This has consequences. While original sin itself is the deprivation of sanctifying grace, it also carries with it a fallen and corrupt nature, which is the stain of original sin.
To give a comparison, suppose God created man in an elevated state in which we were endowed not only with the arms and legs that are proper to our nature, but also with an added gift of wings. Suppose then that Adam and Eve did something that not only cost them their own power of flight, but also caused their offspring to be born with stubby, non-functional wings. This would cause problems for human nature, and even if God later restored wings to individual believers as an act of grace, we still could suffer problems from the genetic damage that had cost us our flight in the first place.