Native speaker. Lide is never pronounced like that in daily conversation or even i formal speak. It is pronounced more like Lee.
Could you confirm that in the expression "kan godt lide", "lide" is pronounced more like "lee", but when "lide" is used as the verb "at lide" meaning "to suffer", the Danish "d" is pronounced? Based on http://ordnet.dk/ddo/ordbog?query=lide&tab=for
Hvordan skriver man "Could you like the surprise?" på dansk?
"could you like ..." is bad English and nobody would say that.
Lide means to suffer. Kunne...lide means to like
Yes, like also in German or Russian!
German: to suffer = leiden; to like = leiden können (can suffer)
Russian: to suffer = terpet'; to like = moč' terpet' (can suffer)
You see, this is not just a Danish thing.