L’David Hashem without Shacharis

Should someone who does not Doven Shacharis, e.g. a mother of young children, still say L’David Hashem in the morning? Is there a special value in saying it on its own during Elul, or is it only a Perek Tehilim when not succeeding the Dovening? Thank you

ב"ה Shalom In the sefer "Tzlota d'avraham" (Vol. I, pg. 402) which is a siddur with a very thorough commentary, the author says that the "mekubalim" who set the custom to say "ledavid" did not make clear rules of where exactly in the tefilla it should be said therefore there are different customs. According to the Mekubalim there is a special value in saying it on its own during Elul. Although,It may be that according to these same Mekubalim there is an added value when said after Shmoneh Esreh , but that should not stop us from saying it even on its own. Chodesh Tov