If the club limited its membership, it will have to raise its dues is not ordinarily a grammatical construction. For it to be grammatical you would have to be speaking of an uncertain but possible past condition with a necessary future consequence:
I don't know whether the club limited its membership last year; but if it limited its membership then it is certain that it will have to raise its dues in the future.
It is more likely that you are speaking of a present possibility—will the club limit its membership or not? And what will be the consequence if it does? If you think it is possible, then you are dealing with a realis (real) situation: you will use the simple present form of limit in the condition (IF) clause and a simple future form of will in the consequence (THEN) clause.
The club is now saying that if it limits its membership it will have to raise its dues.**
If you think it is not possible that it is not possible that the club will limit its membership you are dealing with an irrealis (unreal) situation: you will use the past form of limit in the condition clause and the past form of will in the consequence clause. The past forms here mark serve as markers of irreality:
The club will not limit its membership now because if it limited its membership it would have to raise its dues.
If, however, you are speaking of a realis past possibility—something the club was thinking about last year, for instance—you also use the past forms of limit and will. Here the past forms mark past tense rather than irreality.
The club said last year that if it limited its membership it would have to raise its dues.
And if you are speaking of an irrealis past situation—one you know did not come to pass—you use what looks like a perfect construction to mark this as past irrealis:
The club did not limit its membership last year because if it had limited its membership it would have had to raise its dues.