Why does tensor formulation of Lorentz force law guarantee Lorentz invariance?

The Lorentz force law is $$vec{F}=q(vec{E}+vec{v}timesvec{B}).$$
In tensor formulation, it is
$$f^mu=qU^lambda {F_lambda}^mu.$$

In Sean Carroll’s spacetime and geometry book, pg. 32-33, he said that

the requirement that the equation be tensorial, is one way of guaranteeing Lorentz invariance.

What does he mean by Lorentz invariance here?

I know that in a Lorentz transformed coordinate $x’^{mu} $, the tensor equation will be simply $$f’^mu=qU’^lambda {F’_lambda}^mu.$$
However, that is Lorentz covariance if I am correct. What does the author mean by Lorentz invariance?