I think most of the people who answered this missed the point of the quote.
"Everybody should get married atleast once in their life time, No one deserves to be happy all their life"
Means if you are married, then you will be unhappy during the marriage.
I think he's quoting the viewpoint of a cynic who's had bad marriages. A lot are bad like that because many people are immature in relationships, and marry for the wrong reasons, but at the same time, some people end up in really good marriages which do not break apart like that.
On the flip side though, no marriage is perfect, so all will have problems, then again life is the same (although I do not believe this interpretation was considered by the writer).
Assuming you are judging true or false on the basis of "everyone needs to experience something which may not be pleasant but is a part of life" (and not whether marriage is or is not bad), then I would say the statement is true to an extent (I agree, but I do not think anyone should be forced to do anything, only advised, hence I disagree with the use of "should").
Convuluted answer I suppose, but given how Lord Bryon worded it, there are a few different things to say.
Or to paraphrase;
True, but I think he's being overly cynical and has debateable premises for his argument.