Keywords: propranolol, lipid emulsion (PubMed Search)
There have been a variety of case reports that have been describing the effects of lipid emulsion therapy on severe hemodynamic overdoses. As time has gone on, we have realized that this therapy is not for all severe overdoses. The type of medication and its pharmacokinetic properties factor into the decision. There is minimal evidence and no ideal randomized control trials that will tell us what the right answer is but take beta-blockers for instance:
Atenolol - in overdose, consider hemodialysis, very effectively removed by HD 
Propranolol - very lipophilic and one of the few beta-blockers that can cause widened QRS, seizures as well as the prototypical hypotension and bradycardia.
Because of its lipophilicity, ability to cross the blood brain barrier and ability to cause lethal dysrrthmias, lipid emulsion therapy has been effective in reversing the clinically severe effects of a propranolol overdose. 
Huang SH, Tirona RG, Ross C, Suri RS.
Hemodial Int. 2013 Oct;17(4):652-5. doi: 10.1111/hdi.12020. Epub 2013 Jan 24.
Jovic-Stosic J, Gligic B, Putic V, Brajkovic G, Spasic R.
Clin Toxicol (Phila). 2011 Jun;49(5):426-30. doi: 10.3109/15563650.2011.583251.