If I understand you, you are asking why 1x was improved but not LTE?
According to the specs of your equipment, 1x (CDMA) is called out as a specifically supported technology, on a specifically supported frequency. LTE is not mentioned (because of the age of the equipment), Although whether that alone would be definitive in the case of a simple repeater I couldn't say. I can tell you however, that the actual frequencies used by the most widely deployed Sprint LTE (PCS G-Block), are not compatible to your equipment.