A horse with a very hollow side - for instance on the right - will often lope a little faster that direction because the horse overbends and is not in balance. Often they will drop their shoulder which, in turn, will cause their left hip (in this example) to go to the outside.
On the opposite side, the horse often travels in a less cadenced manner and will often have trouble reaching up deep with his inside hind leg causing his body to appear stiff and straight. Most horses look their best with a slight arc to the inside (very slight, I tell my riders they should only barely see the in-side of their horse's eye) so this stiffness, caused by the hollow side, makes the lope less pleasing to ride and to look at. Every horse is different and some do need to be a bit straighter than others so good judgement is also part of this exercise.
Now, when the horse becomes properly supple and balanced, the quality of the lope will definitely improve and so will his speed. The horse will round up, lift his back and slow down. But remember that they cannot do this if they're too stiff or too "hollow" because then they cannot balance.
So.... I teach that balance is not only back to front but also (and this is so important!) from side to side. If for instance, a horse is leaning on your leg or your rein, he is not balanced. Some work that can help you with your horse's balance include a series of spiralled circles (first large, then with your outer leg, pushing the horse into a small circle, than back out again into a large circle - careful to keep the spirals circles - no ovals or stop signs!). Also, leg-yields and counter canters and reverse arcs can help to lift the shoulder and build balance. I always work both sides but I like to start with the stiff side, then the good side, then back to the stiff side again.
As I said a few weeks ago though, none of these exercises are "one hit wonders" - you have to stick with a program to see results. Think about which warm-up exercises will help your horse the most and work them in every time you ride. I hope this quick tip helps with your next ride! Talk to you next week. JD