Yeast need a trace amount of oxygen in an anaerobic fermentation such as brewing to produce lipids in the cell wall. With out O2 the cell cannot metabolize the squalene to the next step which is a lipid. The lipids make the cell wall elastic and fluid. This allows the mother cell to produce babies, buds, in the early part of the fermentation and keeps the cell wall fluid as the alcohol level increases. With out lipids the cell wall becomes leathery and prevents bud from being formed at the beginning of the fermentation and slows down the sugar from transporting into the cell and prevents the alcohol from transporting out of the cell near the end of the fermentation. The alcohol level builds up inside the cell and becomes toxic then deadly.
Lallemand packs the maximum amount of lipids into the cell wall that is possible during the aerobic production of the yeast at the factory. When you inoculate this yeast into a starter or into the mash, the yeast can double about three time before it runs out of lipids and the growth will stop. There is about 5% lipids in the dry yeast.
In a very general view:
At each doubling it will split the lipids with out making more lipids (no O2). The first split leaves 2.5% for each daughter cell. The second split leaves 1.25% for each daughter cell. The next split leaves 0.63%. This is the low level that stops yeast multiplication. Unless you add O2 the reproduction will stop.
When you produce 3-5% alcohol beer this is no problem. It is when you produce higher alcohol beer or inoculate at a lower rate, that you need to add O2 to produce more yeast and for alcohol tolerance near the end of fermentation. You definitely need added O2 when you reuse the yeast for the next inoculum.
If you prepare a starter culture you will need added O2. in the starter and perhaps in the main mash as a precaution. You will need to follow the precautions as mentioned above. If the mash is designed to produce 3-5% alcohol you may not need added O2. Brewing above that needs added O2.
Regarding your comment about growing your own yeast that will not need added O2 in the fermenter; The Lallemand yeast factory grows yeast under a different metabolic pathway than you will have in your starter culture. We feed the media to the aerobic fermentation at a rate that will keep the sugar levels below 0.2% at all times to maintain the Pasteur Effect. This builds cell mass with minimum to no alcohol production. As the sugar level rises above 0.2% the Crabtree Effect begins and no matter how much air you feed the fermentation, alcohol + CO2 are the main by-products. Your starter culture will have a much higher level of sugar. You will produce some cell mass but mostly alcohol and CO2 no matter how much air you add by stirrer or bubbles.
Dr. Clayton Cone