The Longest Common Subsequence (LCS) is one of the most basic similarity measures and it captures important applications in bioinformatics and text analysis. Following the SETH-based nearly-quadratic time lower bounds for LCS from recent years [4, 22, 5, 3], it is a major open problem to understand the complexity of approximate LCS. In the last ITCS  drew an interesting connection between this problem and the area of circuit complexity: they proved that approximation algorithms for LCS in deterministic truly-subquadratic time imply new circuit lower bounds (ENP does not have non-uniform linear-size Valiant Series Parallel circuits). In this work, we strengthen this connection between approximate LCS and circuit complexity by applying the Distributed PCP framework of . We obtain a reduction that holds against much larger approximation factors (super-constant, as opposed to 1 + o(1) in ), yields a lower bound for a larger class of circuits (linear-size NC1), and is also easier to analyze.