The Lorentz factor is a particular case of a factor which depends on the angle between space and time, for example to find the $\gamma$ factor directly, we use the Pythagore theorem $\vec{c}^{2}t'^{2}=\vec{v}^{2}t'^{2}+\vec{c_{0}}^{2}t^{2}$$,\;\;|\vec{c}|=|\vec{c_{0}}|=c$ (the case where $\vec{c}_{0}\perp \vec{v}$, i.e. the observer moves orthogonally away from the event ), in the ca where it is $\,\vec{c}\perp \vec{v} \,$ we have $K=\frac{1}{\sqrt{1+\frac{v^{2}}{c^{2}}}}\,$(i.e. the observer approaches the event orthogonally ).
So the calculation of the length depends on the angle and direction of the observer in relation to the event.