  Both ab-plane and c-axis thermal conductivities ($\kappa_{ab}$ and
$\kappa_c$) of lightly doped La$_{2-x}$Sr$_x$CuO$_4$ and
La$_2$Cu$_{1-y}$Zn$_y$O$_4$ single crystals ($x$ or $y$ = 0 -- 0.04) are
measured from 2 to 300 K. It is found that the low-temperature phonon peak (at
20 -- 25 K) is significantly suppressed upon Sr or Zn doping even at very low
doping, though its precise doping dependences show interesting differences
between the Sr and Zn dopants, or between the $ab$ plane and the c axis. Most
notably, the phonon peak in $\kappa_c$ decreases much more quickly with Sr
doping than with Zn doping, while the phonon-peak suppression in $\kappa_{ab}$
shows an opposite trend. It is discussed that the scattering of phonons by
stripes is playing an important role in the damping of the phonon heat
transport in lightly doped LSCO, in which static spin stripes has been observed
by neutron scattering. We also show $\kappa_{ab}$ and $\kappa_c$ data of
La$_{1.28}$Nd$_{0.6}$Sr$_{0.12}$CuO$_4$ and
La$_{1.68}$Eu$_{0.2}$Sr$_{0.12}$CuO$_4$ single crystals to compare with the
data of the lightly doped crystals for the discussion of the role of stripes.
At high temperature, the magnon peak (i.e., the peak caused by the spin heat
transport near the N\'{e}el temperature) in $\kappa_{ab}(T)$ is found to be
rather robust against Zn doping, while it completely disappears with only 1% of
Sr doping.
