I am not a doctor. I worked adult and pediatric critical care units over 10 years ago so have been out of the field for a while. So I preface by saying that.
If your Dad is oxygenating and has a normal O2 sat (oxygen saturation) then he would not need oxygen. Having oxygen on standby in case his oxygen saturation levels did fall and he need oxygen would be wise to have oxygen on standby. Just from the the brief history you shared it seems because of the statement of the neurologist saying his left diaphram is weak that the innveration to this portion of his diaphram is affected therefore he cannot ventilate/breathe as well because it is a mechanical problem. If he can't ventilate well CO2(carbon dioxide) will build up and eventually oxygen saturation levels fall when there is too much of a CO2 build up. His oxygen saturation can be monitored by a pulse oxymeter at home.
I don't have first hand knowledge of these but here are some links you could research on treatments for ALS (I am no expert on ALS not have vast knowledge of it.........my mother in law did pass away from it years ago)