Creating 1L of 1000 ppb stock solution of Pb2+
Making the solution in a single step is inaccurate up to impossible.


Try to find a crystal of lead nitrate with the mass close enough to $\pu{1 mg}$
Try to weight up $\pu{1 mg}$ on scales with good enough accuracy.
Try to make such $\pu{1 ppm}$ solution stable enough.


The usual thing is to create a concentrated stock solution ( e.g $\pu{1000 ppm}$ and creating the working solution in 1 (1000 times) or 2 step ( 20x50 times) dilution whenever needed.

There is need to consider stabilizing by an acid, to prevent hydrolysis and adsorption. Very diluted solutions, like for AAS, are often stored in PE instead of laboratory glass to prevent ion Vs glass surface interactions.