well, it depends on a few things, but let me give you some tipps:
build the pyramids and get representation! this is even more useful in LoR than in normal civ, because it also eliminates a big factor of instability.
use garrisons to force some stability in endangered cities. this works also well with monarchy which then gives an extra happiness stability effect.
do not overexpand early on. distance penalty can accumulate. prioritise distance techs (though it is not fully clear which ones they are).
be careful with attacking. conquered cities are automatically very unstable.
watch out for slavery. although useful and even essential for some play styles ( I think), with LoR there is an added instability price tag. for starters, maybe refrain from it.
religion: can be good, but if you have more than one and a state religion, it can get messy. you may want to consider inquisitors.
in war, loosing a critical food resource can lead to starvation either directly or indirectly. same for happiness resources. you may need to play a bit more careful and leave happiness buffers. otherwise, endangered cities can become rebellious.
avoid a bad financial situation. this is if you are at or below 50% gold and are still negative. such things can also get very ugly.
avoid the initial revolution at all cost! once you slip in, it is very (!) hard to get out again. this imo is a real weakness of the package and should be addressed at some point.
lastly, when you are at the level, use revolutions to your advantage. your biggest competitors are often also large empiries, sometimes borne of conquest. look in the statistics graphs whether they have bad nationwise stability. if yes, use spies to sabotage some potentiall critical cities, e.g. via food poisoning, forment unhappiness or destroying resource improvements. if you keep it up, you may be able to launch a chain reaction that tears the empire apart. which leaves you to pick up the weakened, warring pieces
.
in general. there is a learning curve connected to it. but if you make it through, a really great addition awaits you.
