You can use logsave command to save the output of a command in a logfile. General syntax is as follows:
logsave /path/to/logfile command-name argument(s)

The logsave program will execute command-name with the specified argument(s), and save a copy of its output to logfile. If the containing directory for logfile does not exist, logsave will accumulate the output in memory until it can be written out. A copy of the output will also be written to standard output. If command-name is a single hyphen (-), then instead of executing a program, logsave will take its input from standard input and save it in logfile

logsave is useful for saving the output of initial boot scripts until the /var partition is mounted, so the output can be written to /var/log. For example, save output of ls command to output.log file:
logsave /tmp/output.txt ls
For example run lftp and save remote server file list to /tmp/filelist.txt for other scripts:
logsave /tmp/filelist.txt 'lftp -u -e "cd pub;ls;quit;" admin,mypassword ftp.nixcraft.in '