The authors study the following lattice system of Fisher-KPP type (with Dirichlet boundary condition at \(n=0\)): \[ u'_n(t)=u_{n+1}(t)-2u_n(t)+u_{n-1}(t)+f(u_n(t)), \quad n\in \mathbb{Z}. \] They first establish the existence of a unique positive stationary solution \(\{u_n\}\) and show its stability. Then they construct two types of entire solutions, the first converging to \(\{u_n\}\) as \(t\rightarrow +\infty\), the second converging to zero locally uniformly with respect to \(n\) as \(t\rightarrow -\infty\). The difference is that, in a moving frame, as \(t\rightarrow -\infty\), each solution of the first type converges to a traveling wave solution, while each solution of the second type converges to a horizontal line. To show the essential property \(u_{\infty}(t)\equiv1\) for the second type of entire solutions, they investigate the eigenvalues of a suitable matrix. This is a completely different approach from the Fourier transformation's method used for continuous systems.