I fail to see how this setup is not fair - but more importantly, I fail to see how LDT is losing in this situation. If the payoff matrix is CC:2/2, CD:0/3, DD: 1/1, then if LDT cooperates in every round it will get $~$99\cdot 2=198$~$ utilons, while if it defected then it gets $~$100$~$ utilons.
Thus $~$LDT$~$ wins $~$198$~$ utilons in this situation, while a CDT agent in his shoes would win $~$100$~$ utilons by defecting each round.
The situation changes if the payoff becomes Having a higher score that CDT: $~$1$~$, while Having an equal or lower score than CDT: $~$0$~$.
Then the game is clearly rigged, as there is no deterministic strategy that LDT could follow that would lead to a win. But neither could CDT win if it was pitted in the same situation.