We show that a dynamically convex Reeb flow on the standard tight lens space
(
L
(
p
,
1
)
,
ξ
s
t
d
)
(L(p, 1),\xi _\mathrm {std})
,
p
>
1
,
p>1,
admits a
p
p
-unknotted closed Reeb orbit
P
P
which is the binding of a rational open book decomposition with disk-like pages. Each page is a rational global surface of section for the Reeb flow and the Conley-Zehnder index of the
p
p
th iterate of
P
P
is
3
3
. We also check dynamical convexity in the Hénon-Heiles system for low positive energies. In this case the rational open book decomposition follows from the fact that the sphere-like component of the energy surface admits a
Z
3
\mathbb {Z}_3
-symmetric periodic orbit and the flow descends to a Reeb flow on the standard tight
(
L
(
3
,
2
)
,
ξ
s
t
d
)
(L(3,2),\xi _\mathrm {std})
.