There are conservatives who lie and there are liberals who lie. Neither blue nor red has a monopoly on truth-tellers.
However, unless one denies that there are distinctive values on the right and on the left -- a proposition that no serious liberal or conservative would deny -- how much truth is valued may be different for the right and the left.
In the hierarchy of leftist (as opposed to traditional liberal) values, truth is below other values, such as equality, opposition to war, the promotion of secularism and a number of other highly regarded values on the left.
This does not mean that the number of truth-tellers among individuals on the left is necessarily smaller than the number of individual truth-tellers on the right. It means that truth-telling is not high on the left's list of values.
Since this is, obviously, a generalization, and a negative one at that, anyone who makes this generalization is obligated to provide arguments and examples.
The first example is what is known as political correctness. Leftist denial of what is true is so widespread that we have a term for it, political correctness. There is no comparable right-wing political correctness, i.e., denying truths so as not to offend right-wing values or certain groups.
For example, among many on the left, especially academics, it has been almost impossible for decades to tell the truth about the innate differences between men and women because of the leftist dogma of innate similarities between the sexes. So deep is the left's hostility to truth regarding the sexes that a president of Harvard University was forced from office after suggesting that men's and women's brains process math and some science differently.
Similarly, many leftist professors at Duke University used the false rape charges against three white lacrosse players to reinforce the left-wing belief (itself not true) that America is racist. The truth was not nearly as important to them as proving how racist whites are.
Textbooks. A prime example of the left's view of truth is its changing the goal of high school American history textbooks from telling truth to promoting self-esteem among minority and female students by depicting more women and more non-whites in American history textbooks.