No. When heated, baking soda (sodium bicarbonate) doesn't turn into lye – it breaks down into soda ash (sodium carbonate), water, and carbon dioxide.
Dissolving the resulting soda ash in water gives you a soda solution – not lye. You can still use this soda solution for pretzel-style baked goods, but the effect is weaker: the result is less dark and glossy, and the flavor is less intensely "lye pretzel"-like.
The reason lies in base strength: true lye contains sodium hydroxide (NaOH), a much stronger base than the sodium carbonate in a soda solution. This stronger basicity is exactly what produces the typical brown, glossy crust when baking – and it's also what makes real lye considerably more hazardous to handle.
Historically, true lye was actually made from a soda solution – just with one extra step: the soda solution was reacted with slaked lime (calcium hydroxide). This produces sodium hydroxide, while the resulting calcium carbonate precipitates as an insoluble solid and can be separated out. This process, called causticization, was the standard method for producing lye for centuries, before it was largely replaced in the 20th century by chlor-alkali electrolysis.