To solve this problem, we need to determine the least number of lines, $k$, required to ensure that any Colombian configuration of 4027 points (where 2013 are red and 2014 are blue, with no three points collinear) can be separated such that no region contains points of both colors.

The steps to find the solution are as follows:

### Step 1: Understanding the Requirements

1. Colombian Configuration: We are given 2013 red points and 2014 blue points, with no three points collinear.
2. Properties of the Arrangement:
- Lines do not intersect points: None of the lines should pass through any of the given points.
- Single color per region: Each region created by the lines must contain points of only one color.

### Step 2: Analyzing the Problem

We need to separate 2013 red points from 2014 blue points using the least number of lines. A crucial observation here is that to separate two groups of points in the plane, we can draw lines in a manner analogous to drawing a linear separator, ensuring that one group is entirely on one side of the line and the other group is on the opposite side.

### Step 3: Strategy with Minimum Lines

For every point, we can use lines to isolate each point of one color away from points of the opposite color. Since we are dealing with 2013 red points, we will aim to surround each point to separate it from the opposite color. To effectively surround each red point so that no blue points are allowed in-between, we can conceptualize needing $k = 2013$ lines covering potential linear separators.

### Step 4: Finding the Minimum Number of Lines

Given that for every red point to be completely isolated from being in the same region as a blue point, we have potentially $k = 2013$ necessary lines in the worst-case distribution of points due to the following reasons:

- The minimum $k$ lines is needed such that these lines can separate each red point effectively from all blue points.
- Any configuration with fewer than 2013 lines risks a region containing both red and blue points as the density and placement may cluster more densely, exceeding half with both points.

Therefore, the least number $k$ of lines needed is:

$$\boxed{2013}$$

By using 2013 lines wisely, we can ensure that all regions after demarcation contain points of only one color, satisfying both conditions for any Colombian configuration. The value of 2013, therefore, captures the worst-case scenario configurations, ensuring all potential configurations can be addressed.