I will sometimes do my sprints at lunch after lifting heavy in the hours before work. I can do fine on my sprints if I wait that long. The other day I did my sprints right after my lifting. This time around I did 3 sets of 25 with lower weights on my squats rather than the heavy weight kind. I could only get 6 sprints in and the last one was so slow it was barely more than a jog.
For the person who asked about Smith machine, don't use the Smith machine. If you have safety bars on the squat, you can fail gracefully. Just make sure they are high enough you can crawl out from under the barbell. I've gotten rather embarrassingly stuck a few times.
Female, 5'3", 50, Max squat: 202.5lbs. Max deadlift: 225 x 3.