The German "Lasst es Euch schmecken" or "Lassen Sie's sich schmecken" (familiar/polite) is used in a casual way instead of "Guten Appetit" or "Mahlzeit (casual, regional)" at the beginning of a meal.
To "tuck in", to my knowledge, is used to tuck somebody's sheets in at bed time. A similar sounding equivalent to "Lasst es Euch schmecken" could be "dig in" instead:
[ in imperative ] (dig in) informal used to encourage someone to start eating with gusto and have as much as they want: put the sausage on top of the polenta; then dig in. (From the New Oxford American Dictionary)