Yes, your Warforged player can walk along the bottom of the lake without making Swim checks - there's a whole terrain description for that.
In the Underwater Combat section of the terrain description, there's a table which specifies that a creature with "Firm footing" can move at half speed even without a Swim check.
Creatures have firm footing when walking along the bottom, braced against a ship’s hull, or the like. A creature can only walk along the bottom if it wears or carries enough gear to weigh itself down—at least 16 pounds for Medium creatures...
A warforged's plating is probably enough to qualify as "enough gear to weigh itself down" (especially the Adamantine plating,due to the Swim penalty, though that's a GM call; either way, keep it consistent!), and my experience says that, aside from the odd monk, most medium characters have 16+ pounds of "stuff" on them while they're adventuring.
Note that, while the warforged would be able to walk indefinitely, it is entirely possible that they will get lost without some method of avoiding that fate (including just being able to see their destination, too).