In "CLASSICAL ELECTRODYNAMICS" by J.D.Jackson, 3rd Edition , $\S$ 11.3, the
 author gives in equation (11.19) a generalization of  Lorentz transformation as follows :  


If the axes in K and K' **remain parallel**, but the velocity $\:\mathbf{v}\:$ of the frame
K' in frame K is in an arbitrary direction, the generalization of (11.16) is 

$$
\begin{align}
x'_{0} & =\gamma\left(x_{0}-\boldsymbol{\beta}\boldsymbol{\cdot}\mathbf{x}\right)\\
\mathbf{x}^{\prime} & = \mathbf{x} +\dfrac{\left(\gamma-1\right)}{\beta^{2}}\left(\boldsymbol{\beta}\boldsymbol{\cdot}\mathbf{x} \right)\boldsymbol{\beta}-\gamma\boldsymbol{\beta}x_{0}
\end{align}
\Biggr\}
\tag{11.19}
$$
where
$$
\begin{align}
\boldsymbol{\beta} & = \dfrac{\mathbf{v}}{c}\; \qquad  \beta=|\boldsymbol{\beta}| \\
\gamma &=\left(1-\beta^2 \right)^{-1/2}
\end{align}
\tag{11.17}
$$

and
$$
\begin{align}
x'_{0} & =\gamma\left(x_{0}-\beta x_{1}\right)\\
x'_{1} & =\gamma\left(x_{1}-\beta x_{0}\right)\\
x'_{2} & =x_{2}\\
x'_{3} & =x_{3}
\end{align}
\Biggr\}
\tag{11.16}
$$
the Lorentz Transformation with the velocity $\:\mathbf{v}\:$ parallel to the common $\:x-x'\:$ axis.  

In case (11-16) it's permissible to talk about **parallel axes**. But in the generalized case (11-19) is it permissible to talk about **parallel axes ?** What is the meaning of parallelism in this later case ?