The party was not in any agreement on this Bukharin probably represented the majority of the party on this which was for revolutionary war. Trotsky was sent to delay negotiations initially, while Lenin was circling questions to the soldiers if they would support revolutionary war https://twitter.com/notXiangyu/status/1334121500207689731

As well as having the army inspected, IIRC Nikolai Krylenko
was supposed to give a report on if he thought revolutionary war was possible. He also in December conducted a survey asking soldiers what they thought should be done, and they answered drag the treaty out and make

unfavorable peace if needed as the army could not defend Petrograd.

The party including Lenin struggled with the question and it was thought by many that it would be an agreement with imperialists and a betrayal to make a peace with the Germans. Trotsky in several speeches can be seen wavering on this as Lenin did as well.

When it become impossible to delay Trotsky wrote back to Lenin, and he called for a recess to return to find out what the Soviet Government wanted to do.

Trotsky's proposal actually got more then Lenin, but both men lost to the Bolshevik left who advocated revolutionary war

Trotsky's proposal is the one that won in the end, because it was a compromise, so no he didn't carry out his own policy without party approval. Lenin was for a annexationist peace at this point, but he was in a firm minority.

Bukharin was the revolutionary war guy and he probably ha the majority support of the party not Lenin or Trotsky.

Trotsky policy was endorsed by the CEC, he did butt heads with Lenin as he thought the Germans were bluffing about a new offensive, possible in part because Trotsky knew Germany wanted to free troops from the eastern front to crush France before the US arrived.

Can see here Trotsky did butt heads with Lenin, but Lenin again was in an extreme minority on this and it is clear Trotsky thought the Germans were bluffing still

In the end Trotsky honored his agreement with Lenin on it.