"Ej" is a synonym of "Inte", but a little more formal and older and is often used on signs where something is forbidden.
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Example:
Do not worry = "Oroa dig ej" (Not something you usually say, but it is possible)
Don't worry = "Oroa dig inte"
It is not permitted to run in the hallway = "Det är ej tillåtet att springa i korridoren"
Regarding your sentence; it's another way of saying "Vi skall INTE falla utan sorg" (We shall NOT fall without sadness/We shall NOT go under without sadness). As "Ej" comes first in the sentence it means that it's stressed that it is the most important part in the sentence.