I'm not sure the question should be "to lift or not to lift," but rather how to best utilize the time in the weight room on a game day. From what I have seen a lifting teacher doesn't have to make some personalized plan for every student as an earlier post suggested. Sure there are sports specific lifts to emphasis but that would be a lot of work to balance all of those routines in the space most weight rooms have. But a good lifting teacher should have the time and ability to recognize what he/she is asking of the students and how that may affect certain athletes who are competing later that day. A good teacher may allowing competition athletes to have some minor adjustments to the lifting routine depending on the normal lifting plan for that day. This would be no different than giving some modifications on an assignments for some students, so I'm sure a teacher that cares to make an effort would be able to handle this. Sadly though I have heard of a few instances where the lifting teacher either did recognize a particularly taxing routine would cause an issue or just didn't care enough to allow for some minor adjustments to me made. I think this is where good communication between the teacher, coaches, and athletes is helpful. But also rather than telling the teacher to not let the athlete lift at all the coach should be open minded to the teacher approach if he/she has a solid background on the subject and can show proof of that their plan is successful to athletes.
Many days the regular lifting routine would be fine for those having a game or not. Heck in many case the lifting teacher isn't asking athletes to push it to the ultimate limit within the hour of actual workout time most of them have. Nor are most students really trying to push themselves to the breaking point over the course of that same hour. Realistically trying to get most of the students to just lift with maximum effort and proper form is a daunting task for most.
However, on a few of those class days the style of lifting could indeed cause some minor issues for an athlete who will have a game later that day. For that the teacher could easily ask those athletes to make a minor adjustment to the number of lifts, the amount of reps, the amount of weight, skip/substitute one of the lifts in the rotation, etc. A lifting teacher with a decent background in exercise science should be able to recognize when he/she has assigned a particularly taxing routine and know what adjustments would be warranted for completion athletes.
So yes based on what I have seen before getting in a good lifting routine and sweat going is helpful to most athletes on game day. Especially when you consider most athletes are spending the majority of the day rest in a school desk. I'm not exercise science expert, but have seen enough lifting plans and talked to enough exercise science guys to know that it more helpful than harmful to do some exercise on a game day. However, a good teacher should be mindful enough of what he/she is planning to know if that routine could be a possible detriment to the athletes competition performance.