You can enclose the part you want to match in a non-capturing group: (?:). Then it can be treated as a single unit in the regex, and subsequently you can put a ? after it to make it optional. Example:
/Singers?:(.*)\s?(?:Lyricists?:(.*))?/
Note that here the \s? is useless since .* will greedily eat all characters, and no backtracking will be necessary. This also means that the (?:Lyricists?:(.*)) part will never be matched for the same reason. You can use the non-greedy version of .*, .*? along with the $ to fix this:
/Singers?:(.*?)\s*(?:Lyricists?:(.*))?$/
Some extra whitespace ends up captured; this can be removed also, giving a final regex of:
/Singers?:\s*(.*?)\s*(?:Lyricists?:\s*(.*))?$/