Assuming that the lines continue after "Lambda", as suggested by the OP, this command should work:
gawk 'match($0, /execution\stime:([0-9]+)s/, a) && a[1] > 10 { print $0 }' logfile
with 'logfile' being the name of the logfile (/root/.pm2/logs/proxy-out-1.log)
This solution uses the match function to capture the execution time as a parenthesized group, and then bases a numerical comparison on the captured value to decide if the line should be printed.
The longer but more portable version is:
awk 'match($0, /execution time:([0-9]+)s/) && substr($0, RSTART+15, RLENGTH-16 ) > 10 { print }' testfile
