Hopelessly means in a way that offers no chance of success. Hopelessly lost, hopelessly outnumbered, hopelessly in love.
The last of those is the odd one: hopelessly in love is a happy phrase built from a bleak word, and it means beyond any hope of recovery, which is meant as a good thing. Everywhere else the word is plain and bad news.
1adverbhopelesslyIn a way that offers no chance of success.
“Without a map or a phone, we were hopelessly lost in the forest.”
hopelessly is a degree.
From hopeless + -ly.
Etymology from Wiktionary, CC BY-SA