Hi. Yes, this is what a mother would say when sending her son to war. She'd give him the shield and say "either this one, or on it". A loose translation would be "Either bring back your shield, or may your dead body return to me on it". It shows to what extent fleeing was unacceptable in this Spartan society. Upper or lower case is not a matter of grammar in ancient Greek. People in ancient Greece used to write in upper case only. The lower case letters is a later invention. Both are equally correct and acceptable.
Η ΤΑΝ Η ΕΠΙ ΤΑΣ