Bash – Merge Two Lists While Removing Duplicates

I have an embedded linux system using Busybox (OpenWRT) – so commands are limited. I have two files that look like:

first file

aaaaaa
bbbbbb
cccccc
mmmmmm
nnnnnn

second file

mmmmmm
nnnnnn
yyyyyy
zzzzzz

I need to merge these 2 lists into 1 file, and remove the duplicates. I don't have diff (space is limited) so we get to use the great awk, sed, and grep (or other tools that might be included in a standard Busybox instance). Going to a merge file like:

command1 > mylist.merge 
command2 mylist.merge > originallist

is totally ok. It doesn't have to be a single-line command.

Currently defined functions in the instance of Busybox that I am using (default OpenWRT):
[, [[, arping, ash, awk, basename, brctl, bunzip2, bzcat, cat, chgrp, chmod, chown, chroot, clear, cmp,
cp, crond, crontab, cut, date, dd, df, dirname, dmesg, du, echo, egrep, env, expr, false, fgrep, find,
free, fsync, grep, gunzip, gzip, halt, head, hexdump, hostid, hwclock, id, ifconfig, init, insmod, kill,
killall, klogd, less, ln, lock, logger, logread, ls, lsmod, md5sum, mkdir, mkfifo, mknod, mktemp, mount,
mv, nc, netmsg, netstat, nice, nslookup, ntpd, passwd, pgrep, pidof, ping, ping6, pivot_root, pkill,
poweroff, printf, ps, pwd, reboot, reset, rm, rmdir, rmmod, route, sed, seq, sh, sleep, sort,
start-stop-daemon, strings, switch_root, sync, sysctl, syslogd, tail, tar, tee, telnet, telnetd, test,
time, top, touch, tr, traceroute, true, udhcpc, umount, uname, uniq, uptime, vconfig, vi, watchdog, wc,
wget, which, xargs, yes, zcat