The main purpose of this paper is to give stability analysis
and error estimates of the local discontinuous Galerkin (LDG) methods
coupled with three specific implicit-explicit (IMEX) Runge-Kutta
time discretization methods up to third order accuracy,
for solving one-dimensional time-dependent linear fourth order
partial differential equations.
In the time discretization, all the lower order derivative terms
are treated explicitly and
the fourth order derivative term is treated implicitly.
By the aid of energy analysis, we show that the IMEX-LDG schemes
are unconditionally energy stable, in the sense that
the time step $\dt$ is only required to be upper-bounded by a
constant which is independent of the mesh size $h$.
The optimal error estimate is also derived by the aid of
the elliptic projection and the adjoint argument.
Numerical experiments are given to verify that the
corresponding IMEX-LDG schemes can achieve optimal error accuracy.