Ljungberg dropped Shkodran Mustafi from his 18 after last Sunday's 2-2 draw with struggling Norwich, yet Arsenal were still a shambles at the back.
Maupay had already forced Bernd Leno into a one-handed save when Webster struck from a corner after lashing home following Dan Burn's downward header.
Arsenal improved with the introduction of club record signing Nicolas Pepe after half-time and France forward Lacazette lifted the mood by climbing above the Brighton defence to head his side level after Mesut Ozil's first Premier League assist since February.
