Some ideas are given by Bell[1]. The author recommends:
Experiments in this laboratory have shown that mixtures of fluoroboric acid, hydrogen peroxide, and ethylenediaminetetraacetic acid (EDTA) rapidly dissolve lead alloys at room temperature. The addition of EDTA is necessary to prevent the formation of insoluble salts during the dissolution step.
Understanding, and optimizing, nitric acid
Nitric acid performs relatively poorly because the lead nitrate (not any oxide) produced by the reaction has more limited solubility in nitric acid solution than in plain water. This is due to the common ion effect, and also at high concentration to nitric acid being a poorer solvating agent for ions than plain water (as distinct from its power as a reactant).
It follows that to maximize the solubility the acid should indeed be diluted with water. Using lead nitrate solubility data from Ferris[2] and the stoichiometry of the reaction between lead and nitric acid, the salt solubility is limited by the acid if the initial acid (before it reacts) is 21-23 weight% $\ce{HNO3}$ or more, depending slightly on whether the acid is reduced to $\ce{NO}$ or $\ce{NO2}$. With a more dilute acid, including the 1:4 diluted mixture that was actually used, saturation is avoided and the reaction proceeds until either the metal or the acid is exhausted.
References
1.
Harry F. Bell (1973). "Rapid dissolution technique for lead alloys". Anal. Chem., 45, 13, 2296–2297. https://pubs.acs.org/doi/10.1021/ac60335a027.
2.
L. M. Ferris (1960). "Lead nitrate-nitric acid-water system". J. Chem. Eng. Data, 5(3), 242. https://pubs.acs.org/doi/10.1021/ac60335a027.
