L'entente was France, England, Russia and all of the minor powers who sided with them.
Central Powers were Germany, Austria-Hungary, and the powers who sided with them.
Germany wanted the treaty signed as soon as possible to relieve its troops on the Eastern Front and be
able to send them to the Western Front where the Americans were now intervening.
The absolute double nature and double cross of the Kaiser and his government was not expected in the era of "death before dishonor". Also, nationalisn outweighed familial ties. For some reason the nature of the family relationships between all of the waring powers made no difference. Victoria and especially Albert along with their daughter Princess Victoria (the Empress Frederick of Germany) and her husband Frederick III truly thought that a progressive conservative government in all of the related nations would keep a long and lasting peace in Europe. None of them, however, had even imagined that their grandson and son, Kaiser Wilhelm II would be as psychologically unstable and meglomaniacal as he was.
Lenin, as stated above, needed to give the Russian people what they wanted which was and end to conflict and land. Lenin did not have absolute control in the beginning of his "great social expreiment" in Marxism or Communism. He needed the troops home from the Eastern Front to reinforce his position in power by strength of men.
So the treaty of Brest Litvosk was signed at any cost.