The lymphatic system is powered in part by the circulatory system and in part by physical activity (aka "exercise"). Fluid from the blood, minus certain blood products, goes out into the tissues and becomes interstitial fluid. Muscle action dramatically increases the rate at which it gets returned from the tissues to the blood.
This is the mechanism by which the body cleans up most tissues. Except for the brain. The brain has a separate mechanism whereby lymphatic fluid (aka interstitial fluid) gets flushed out, taking wastes with it, only during sleep. This is a primary function of sleep.
Personal firsthand experience suggests that exercise is frequently followed by napping precisely because these are separate systems. Exercise may start this process by flushing out other tissues, but your brain won't get flushed of wastes until you sleep.
If you want to benefit from this research, you will need to have good sleep hygiene in addition to exercising. From what I gather, aerobic exercise is likely to do more good from the perspective of powering the lymphatic system than weight lifting.