It's helpful if you know the lynels' attack patterns, and how to respond. There are tons of options for handling each attack, and it's up to your personal preference and playstyle for what will be most successful for you. For instance, when a lynel abruptly jumps away from you, he's about to breathe fire. I handle this by sidehopping, but people also sprint around it, or parry the fireballs. Also worth noting that as he starts the fire attack, you can quickly sprint behind him, and he will stop the attack. When a lynel does a running attack (sword lynels have two of these, spear and crusher lynels have one), if you dodge and do not trigger a flurry rush to interrupt the animation, you can quickly get behind him while he is braking, and mount without having to stun him. Mounted attacks are handy since they do not take off weapon durability. A lot of people switch to their most powerful weapon once they are on the lynel's back, since it doesn't waste durability, and then change it back after they get thrown off. Also, note that if you are using your bow to stun the lynel, your evasiveness is very poor while you have your bow equipped so make sure you put it away if you're planning on dodging any sudden attacks.
If you're still learning lynels' patterns, I'd recommend staying on the defensive and not rush the fight, until you get more comfortable with how they act.