First of all that's not even remotely true.
Montgomery's career numbers - 571 IP, 92 ERA-, 89 FIP-, 93 xFIP-. Lauer's career numbers - 555 IP, 100 ERA-, 105 FIP-, 106 xFIP-
Montgomery's last 2 seasons - 335 IP, 90 ERA-, 89 FIP-, 89 xFIP-. Lauer's last 2 seasons - 277 IP, 85 ERA-, 105 FIP-, 101 xFIP-
Montgomery has been much better over his career and his significantly better peripheral numbers in 60 more innings the last two seasons.
Second of all. The Cardinals absolutely rake LHP. They had a 131 wRC+ vs LHP last season and a career .353 wOBA against Lauer.