public int numSegments = 5;
public float distortionAmplitude = 1f;
void Update() {
blueline.numPositions = numSegments;
for (int s=0;s<numSegments;s++) {
Vector3 basePos = Mathf.Lerp(start_Line.position, end_Line.position, (float)s / (float)numSegments);
Vector3 randomness = Random.inUnitSphere * distortionAmplitude;
blueline.SetPosition(s, basePos + randomness);
}
}

There are a number of things you can do to tweak this - you can replace the randomness with Perlin noise, you can add a multiplier so that the ends are right in line while the center gets the full random effect - but that’s most of it there.

Vector3 basePos = Mathf.Lerp(start_Line.position, end_Line.position, (float)s / (float)numSegments);
//The best overloaded method match for 'UnityEngine.Mathf.Lerp(float, float, float)' has some invalid arguments.

public Transform start_Line;
public Transform end_Line;
private LineRenderer blueline;
public int numSegments = 5;
public float distortionAmplitude = 1f;
void Start() {
blueline = GetComponent<LineRenderer>();
}
void Update() {
blueline.numPositions = numSegments;
blueline.SetPosition(0, start_Line.position);
blueline.SetPosition(numSegments-1, end_Line.position);
for (int s=1; s < numSegments-1; s++) { // from 1 to numSegments-1 so we don't change start and end positions
float t = ((float) s / (float) numSegments); // Lerp with fraction of distance from start to end
Vector3 basePos = Vector3.Lerp(start_Line.position, end_Line.position, t);
Vector3 randomness = Random.insideUnitSphere * distortionAmplitude; // You might want a different random function that doesn't affect all 3 axis
blueline.SetPosition(s, basePos + randomness);
}
}