If you want an LXC instance to start at system startup you need to use something different than adding the lxc-start command into .bashrc since it requires sudo. You should add the command to /etc/rc.local file which is executed at startup as root. Note that because this file is executed as root you need to avoid putting sudo before the command. See the example:
#!/bin/sh -e
#
# rc.local
#
# This script is executed at the end of each multiuser runlevel.
# Make sure that the script will "exit 0" on success or any other
# value on error.
#
# In order to enable or disable this script just change the execution
# bits.
#
# By default this script does nothing.
# start lxc instance on startup
lxc-start -n my_instance -d
exit 0