To calculate the volume of a 3.45 M lead nitrate solution needed to make 0.990 M solution of 450.0 mL, we can use the dilution equation:

M₁V₁ = M₂V₂

where M₁ is the initial concentration, V₁ is the initial volume, M₂ is the final concentration, and V₂ is the final volume.

Let's rearrange the equation to solve for V₁:

V₁ = (M₂ x V₂)/M₁

Plugging in the values we know:

V₁ = (0.990 M x 450.0 mL)/3.45 M

V₁ = 130.7 mL

Therefore, 130.7 mL of the 3.45 M lead nitrate solution must be diluted to 450.0 mL to obtain a 0.990 M solution.