Charlie may have hit on the intended solution, but I am not sure I agree with his interpretation of the problem. There are 28 primes which do not exceed 107 (or 27 if we exclude 2, which cannot be used since that would leave two odd primes in a line, and hence an even, and nonprime, line sum.
I believe we are required to find a solution in which all 17 of the cells are unique primes (pace Charlie), and one in which the prime 107 occurs (which would have to be in one of the eight sums). There are 37 possible sets of primes (not counting orderings) which sum to 107, so exactly one of these, in some order, must be in any solution. I do not see any easy way to pare down the combinations to reasonable search size.
Also, I am faced with the ambiguous problem statement that we are to find "the lowest primes" meeting some condition, without any further definition: does that mean the lowest sum of the primes in the 3x3 grid, or the lowest sum of all seventeen primes, or the largest number of smallest primes, or WHAT?
Perhaps there is a clever shortcut to a solution, if only we were sure of the task.