I disagree; your logic is flawed.

The system is "fair" in the sense that every individual has the same chances of having the same outcome. Even in the case of a FC piling on - the "exploitation" is merely that if 25 people bid and 24 are all in the same FC; then 23 bidders are "comfortable" with the outcome whether they win or lose - but each bidder has a 4% chance that their number is drawn. So just as #25 might be upset that 1-24 win; 1-24 would likely be just as cheesed if #25 wins instead; so the likelyhood of success is "fair" but how the losers will react to the outcome is different and not a matter of fairness - merely a matter of having lost.

The system in that regard is impartial; the randomizer has the same likelyhood of drawing #25 as it does any other number and no individual of the 25 is considered more likely (favoritism/discrimination). It is "just" largely depending on how you see what justice is - as many argue its just a synonym to "fair" - morals being a latter discussion based on your own personal philosophical belief.

A Utilitarian would argue it is not "just" because it is morally reprehensible that #25 should be able to benefit rather then the 24 other souls in the FC; the largest good being the FC winning rather then the individual.

Likewise the Categorical imperative would suggest that provided all are acting in the same regard and not to exempt themselves from the overall outcome; then it would be "fair"; but looking at Kants formulation about selfishness - 1 person putting themselves above 24 others would similarly be deemed "unfair" that they should profit.

Natural law might agree it is unfair however because at its core all players should be offered a identical experience; the problem with applying these maxims boils down to the fact that by the very fact a FC is competing with a private bidder; we are already comparing apples and oranges. If the system were to be "fair" it would not be allowing both parties to bid on the same house; because a FC groups experience should only be compared to the experiences of a FC group and a individuals experiences to those of a individual.

then you got like the 4 flavors of objectivism? But honestly going into depth about the virtue of selfishness and Ayn Rand I would rather not ramble much longer; only to try and point out where I feel the lotto is callous and impartial; but generally is "just" and "fair".

Mind you no system is likely to take into account everyone's circumstances.