This plane can't crash, it doesn't fly

There are $n$ distinct lattice points marked on the 2D plane (2 dimensional).

Find least possible value of $n$, such that we can always choose 2 points out of $n$ points (wherever they may be marked), such that there's at least one more lattice point on the segment joining them.

Details and assumptions:-

$\bullet$ In the 2D plane (or Cartesian plane), every point can be represented as coordinates $(x,y)$, where $x,y \in \mathbb{R}$

$\bullet$ Lattice points are points that have integer coordinates.

Harder versions 3D and 5D