The FBI Uniform Crime Reporting (UCR) Program, the latest year for which statistics are available at time of writing being 2018, gives a breakdown by sex for arrests made during the year.
In particular, for arrests in general, 5,684,385 males were arrested, compared to 2,126,700 females. This represents a ratio of about 2.67 to 1.
With respect to 'crimes of types that motivate the police to use lethal violence', this is a little harder to broadly define, as clearly every arrest is different, but if we use the FBI's definition of violent crime - "offenses of murder and nonnegligent manslaughter, rape, robbery, and aggravated assault" - the figures are 313,411 males arrested compared to 82,854 females, a ratio of about 3.78 to 1.
The only crimes which had a ratio of male arrests to female arrests greater than 5 to 1 were Robbery (5.62), Murder and nonnegligent manslaughter (7.19), Weapons; carrying, possessing, etc. (9.71), Sex offenses (except rape and prostitution) (13.41), and Rape (30.51).
The only crime for which more women were arrested than men was Prostitution and commercialized vice, with 80% more women (15,243) arrested than men (8,456).
Note that arrests are obviously not equivalent to actually committing andor being found guilty of the offense, but are probably a better metric of interaction with police.