Let
K
K
be a complete, algebraically closed, non-Archimedean valued field, and let
P
1
\mathrm {\mathbf {P}}^1
denote the Berkovich projective line over
K
K
. The Lyapunov exponent for a rational map
ϕ
∈
K
(
z
)
\phi \in K(z)
of degree
d
≥
2
d\geq 2
measures the exponential rate of growth along a typical orbit of
ϕ
\phi
. When
ϕ
\phi
is defined over
C
\mathbb {C}
, the Lyapunov exponent is bounded below by
1
2
log
d
\frac {1}{2}\log d
. In this article, we give a lower bound for
L
(
ϕ
)
L(\phi )
for maps
ϕ
\phi
defined over non-Archimedean fields
K
K
. The bound depends only on the degree
d
d
and the Lipschitz constant of
ϕ
\phi
. For maps
ϕ
\phi
whose Julia sets satisfy a certain boundedness condition, we are able to remove the dependence on the Lipschitz constant.