The midfielder, who is out of contract in the summer, showed the Blues just what they would be missing if they let him go with two sharp finishes.
Asked if he knew what the new year would hold, Lampard said: "Nope, I just hope for me personally playing in a winning team.
"I will keep trying to give my best as I've always done when here and will continue to do so.
"I know there's a lot of speculation and talk but for me the enjoyable bit is the 90 minutes."
Everton took the lead early on through Steven Pienaar and hit the woodwork several times, only to come away with nothing.
Lampard admitted the visitors had found the going tough but claimed the win was just reward for their resolve.
He added: "It (the effort) was huge, especially after the sloppy start. The lads dug in, we held our own, rode our luck, but I think we made our own luck and I think we deserved to win it for that.
"To be able to contribute, get the goals, is great, but the team performance deserves most credit."
Chelsea manager Rafa Benitez refused to shed any light on the situation.
"Lampard is a great player, a good professional, who is doing well for us and I will try to bring the best out of him until the end of the season," said Benitez.
"He is one of the players who if he gets in the box he can be dangerous.
"He is under contract. He has shown his full commitment. He is a great player and my job is to keep him fit, happy and scoring goals.
Benitez also refused to comment on speculation the club had entered negotiations to sign Newcastle striker Demba Ba.
"We don't talk about our business in public. My job is to prepare for the games, enjoy them if we win and then after they (the club) will let me know what is going to happen," he said.
"He is a player who is playing for another team so I don't like to talk about other players."