So I cannot claim to know very much about Syliras, and much of what goes on with the city, becuase it is not a city I pay attention to.
However, I was looking at the lore and this is what I found. In the lore, it states that a PC squire does not have to pay LE becuase the knights pay it for them.
When playing a Squire, your Seasonal expense is handled by the Knights, though your living conditions are considered Common; Squires live in communal barracks, and the food provided is more than enough to keep you healthy but it's nothing at all fancy.
This has me thinking that if you are a PC knight training an NPC squire, you may need to pay their LE (which would be common).
From what I gather, you'll only have to pay a Common LE for this NPC during the seasons that you write with him (flashbacks or present). If there is another resource on this, I don't know about it. Hope this helps!