"Conservative" just means on the side that wants to preserve the status quo, but modern conservatism is a particular ideology that does not line up with what was the conservative position in the past always. For example, Jefferson was not a conservative at all in his own time but his overall philosophy is much closer to the GOP than the modern Democratic Party. Another example is in Europe when the capitalists were the liberals and the monarchists were the conservatives. Don't confuse conservatism the ideology with conservatism the upholding of the current order.
But Lincoln was the liberal of the day, like Jefferson, wherever their bases may have been.
Lincoln called himself a conservative in the Cooper Union speech and decisively declared the Democrats to not be conservatives.