There is a management company, but your LLC hired them and is responsible for their actions. Nobody can be stopped from suing the LLC just because it hired another company. Now if the LLC loses a court case because of actions of the management company, the LLC can sue the management company.
And there's the difference between "my LLC can be sued" and "I can be sued". Your LLC can be sued. If it owns say debt free property worth $1,000,000 and the LLC gets sued for $1,000,000 and loses, the properties are gone, the LLC is worthless. If the LLC gets sued for $2,000,000 and loses the properties are gone, the LLC is worthless, but nobody, including you, has to pay the remaining $1,000,000.
You can personally be sued (under the rule that anyone can sue anyone). You can be successfully sued under very rare circumstances, if your personal behaviour is so bad that the law doesn't allow you to hide behind the LLC. For example if instead of allowing a tenant to keep a dog, you allow them to keep a tiger, and the tiger kills someone. Or if a tenant fails to pay, and you beat them up with a baseball bat. Or possibly if you were repeatedly informed that the management company is run by crooks who regularly have endangered tenants and you stopped your LLC from firing them, because they are cheap.
Edit: This was about personal liability. Obviously you will try to deflect damage from the LLC as well.