Is Riot okay with the dominance of Luden's Echo on mages?

is easily the most popular first item for almost every mage champion. It gives you everything you need: AP, mana, CDR, extra burst, and extra waveclear.

Does it need a nerf? Or do the other Lost Chapter upgrades ( ) need buffs?

To me, it seems like the three upgrades of Lost Chapter should be equivalent choices. Picking one over the other should depend on the champion you are playing and your matchup. Right now, there's no contest.

The fantasy of Luden's Echo is that you get an extra spell effect on your casts which is up fairly often. This gives you disproportionately more damage compared to the other options, yet Luden's also gives you the most AP out of all of them. Perhaps reducing the base AP it grants you to help make up for that extra burst would be in order.

GLP gives you a freeze ray on a 40-second cooldown, which is useful for catching people out, setting up skillshots, and escaping from ganks. The cooldown can't really be touched since it's a hextech item, but it might be interesting to allow each bolt to deal damage to a single target (reduced beyond the first bolt, of course, similar to Swain's Q). This would give it a shotgun-like effect that would reward you for getting in point-blank range and give you better self-defense against someone diving you.

Archangel's Staff/Seraph's Embrace is a late-game item that lets you stack up mana and rewards you with a big shield. It's tough to justify buffing this item since it's built on many problematic champions like Ezreal and Ryze. A small nerf to Luden's and a small buff to GLP might be enough to bring the three into line, but if something had to be done for this one, perhaps a small boost in AP or CDR while the shield is on you could make being aggressive with the active more rewarding.