If a significant proportion of a lithium battery was lithium, this would absolutely be true.
By weight, something around 1% of a lithium battery is lithium.
Sodium is seen as an interesting alternative, because there are some indications that it can make that 99% that makes up the rest of the battery lighter. Even though sodium is ~3.5 times worse as a charge carrier, if it's use allows cutting enough weight from that rest, it can be a winner overall.
For example, aluminium is, for complex reasons, not compatible with every part of a li-ion battery, and so they use copper connectors internally, typically containing by weight at least 10 times as much copper as they contain lithium. Sodium batteries can use aluminum everywhere, which saves on not just cost, but also more in weight than the weight difference between equal molar amounts of sodium and lithium.