  The hallmark of Weyl semimetals is the existence of open constant-energy
contours on their surface -- the so-called Fermi arcs -- connecting Weyl
points. Here, we show that for time-reversal symmetric realizations of Weyl
semimetals these Fermi arcs in many cases coexist with closed Fermi pockets
originating from surface Dirac cones pinned to time-reversal invariant momenta.
The existence of Fermi pockets is required for certain Fermi-arc connectivities
due to additional restrictions imposed by the six $\mathbb{Z}_2$ topological
invariants characterizing a generic time-reversal invariant Weyl semimetal. We
show that a change of the Fermi-arc connectivity generally leads to a different
topology of the surface Fermi surface, and identify the half-Heusler compound
LaPtBi under in-plane compressive strain as a material that realizes this
surface Lifshitz transition. We also discuss universal features of this
coexistence in quasi-particle interference spectra.
