The Lonely Runner Conjecture states that if n runners with distinct speeds start at the same point on a unit circle, each runner will be at least 1/n away from the others at some moment. This paper provides a novel constructive analysis framework for this conjecture. We first propose the concept of a "trivial construction" — a speed configuration scheme where all non-zero runner speeds form an arithmetic progression. Using the Pigeonhole Principle, we rigorously prove that for any given threshold 1/n, this trivial construction only requires n+1 runners to ensure that the designated runner is never lonely. Furthermore, through Galilean relative transformations, this result is extended to a situation where all runners are never lonely, proving that the effectiveness of this construction remains valid after multiplying each numerator by any positive rational number. Based on this construction, we introduce a "Time-Position" geometric model, mapping the runner's motion onto a polyline on a plane. By combining features such as constant slope, speed, and the seamless splicing of the region covering the threshold curves, this model intuitively demonstrates the uniqueness and optimality of the trivial construction among all geometric configurations. It provides a solid foundation for rigorously proving that n runners must be lonely. This paper does not prove the original conjecture but provides rigorous results under specific speed configurations.