As to your specific question -- as @Mark Borgioli says, the additional layer of an LLC management company will provide no protection. A tenant is not forced to sue a management company if there is an issue - they can sue the property owner directly. Adding an LLC management company will do nothing more than give the tenant another entity to sue in case of issue. This would result in you getting sued as the owner and you getting sued as an LLC. This would probably be even worse because in most jurisdictions, an LLC cannot be represented in court by a non-lawyer. So, you would not be able to personally respond to a suit against the LLC, you would have to hire an attorney.
In regards to what others are saying, I believe the point being raised is that you state that you cannot buy a house as an LLC because the bank will not give a loan to an LLC without a personal guaranty from you. If you want the LLC protection as an owner, buy it as an LLC and give a personal guaranty to the bank to get the loan. The personal guaranty is not a "liability" issue it is a statement to the bank that you personally will pay the loan even if the LLC has no money. In other words, giving a personal guaranty is the same as getting a loan in your name. There may be other reasons to buy as a person rather than an LLC (interest rate, loan options, whatever) but if the only reason is a desire to avoid a personal guaranty, you are worrying for no reason.
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