Whether LVEF can be increased depends on the underlying causes. Medications returned my EF from below 29% (heart falure range) 6 years ago to currently at 59%.
If the reduced EF is related to a dilated left ventricle (DCM), the dilated LV reduces the contractility of the chamber walls. Therapy for this condition would be to reduce the heart's workload and over a period of time the LV can reverse remodeling (medical term for the phenomonon) to a normal size. It took me about 6 months. The protocol regimen is/was an ACE inhibitor to dilate vessels, beta blocker (coreg) to stabilize heart rate and dilate vessels.
If the low EF is due to heart muscle damage from a prior heart attack, the cells may not have the ability to ever recover and the heart wall is less able to contract with as much force as necessary function normally. Hope this gives you a perspective and if you have any further questions feel free to ask. Thanks for sharing.