My attempt at the FULL lyrics for the Garlean (stolen) anthem.

[Enkidoh]

Not much to go on? Well, I think it implies a lot.
Possibly, this is the anthem used throughout the subjugated territories? It certainly speaks of a coast-to-coast overview. It's certainly a big boast, but it also hides a painful truth for Garlemald; lakes - plural. They weren't fussed with the rivers, or the mountains (though mountains are mentioned in the preceding stanza, so they couldn't use that again ) They focused on Eorzea's lakes.
Now I doubt, when this was written, they saw themselves just being content with Loch Seld. No, though there are many bodies of water in Aldenard, Silvertear Lake is the only one they cared to really own. Possibly this was written just after the occupation began, and they fully expected to lay claim to all of Eorzea. I mean, at that time, Middy was unknown to them.

Now, it could just be that the lyrics were never corrected in light of the setback at Silvertear, or they were deliberately retained as a sort of "don't you dirty Eorzeans get any silly ideas about complacency, ya'hear?" sort of thing. They are saying they'll be back (and, in fairness, they have tried a bunch of times). I'm pretty confident it is the latter; they see Eorzea as theirs, they just haven't been been allowed to pick up the keys, yet.

Well, when you think about it it is true to a certain point, there is a Garlean facility next to Lake Silvertear even before the Calamity (originally Castrum Novus, later Castrum Centri), so they can easily claim "Silvertear is part of Garlean territory!" simply because there is a Castrum there (not that any citizen could or would probably challenge that accuracy openly anyway even if they knew otherwise - the Frumentari would probably see to that quick smart.).

Also I think the use of lake in the plural was simply for dramatic effect, which for propaganda is all important, and is especially here, driving home the Empire's holier-than-thou attitude that all lands potentially belong to them and are simply waiting for the time for Garlemald to arrive and "show them the way".