Ou
awk 'NF<=2 || /Jul/ {next} {print}'
ou
awk 'NR==1 || /Jul/ {next} {print}'
ou, invertendo a lógica para encurtar os comandos,
awk 'NF>2 && !/Jul/ {print}'
ou
awk 'NR!=1 && !/Jul/ {print}'
~$ cat input
first line
Gen second third
Feb second third
Mar second third
Apr second third
May second third
Jun second third
Jul second third
Aug second third
Sep second third
Oct second third
Nov second third
Dec second third
~$ awk 'NF<=2 || /Jul/ {next} {print}' input
Gen second third
Feb second third
Mar second third
Apr second third
May second third
Jun second third
Aug second third
Sep second third
Oct second third
Nov second third
Dec second third
~$ awk 'NR==1 || /Jul/ {next} {print}' input
Gen second third
Feb second third
Mar second third
Apr second third
May second third
Jun second third
Aug second third
Sep second third
Oct second third
Nov second third
Dec second third