It really depends on the type of telepathy you as the author/creator envision. There could be telepathy that is purely intentional, akin to speaking or sign language. If others can always sense your thoughts or emotions, that might more properly be called mind reading or emotional empathy. In the latter, people still might be able to put up walls around their mind to pad or mute the effect. So ultimately, you get to choose.
First, on a communication level, what is truth? What separates truth from a lie? Whether I say the sky is blue or orange, there is nothing inherent in my communication that determines one or the other as real - truth is determined by the facts of life, regardless of what is communicated. The only exception with telepathy or mind reading would be sensing the intention to deceive, and intention is not the same thing as emotion.
You mentioned "evolved" telepathy, so consider what else might have evolved along with that - a subset of related functions that facilitate communication, including "blocking" thoughts or projecting only what is desired. Some might be better at communicating visual imagery, like artists, while musicians would have a much more detailed concept of audio information.
Some might not be good at this - you probably know people in real life who are terrible liars with just words. And anyone can run and jump, but watch the Olympics and tell me you can swim life Phelps. People can train and hone their natural skills to do amazing things, and as a natural ability, I can't imagine this would be an exception.
In response to OP's comment defining his or her brand of telepathy:
Others have answered about "lying" to oneself, so I won't repeat those.
"Feelings" then, must be very precisely defined. Particularly, distinguish between:
Now, some of these things are very low-level, subconscious functionality of the brain. While I always feel emotions and am usually conscious of them, I might not always be conscious of my own motives or intentions. Even if I am self-conscious enough to be aware of them, can I really articulate them, even to myself? Sometimes it takes weeks or months of introspection before one really understands some part of themselves. I personally think it would be unlikely for others to be able to sense those deep things "at a glance," as they aren't really feelings.
I might have strong emotional feelings for someone, but may have no intention of starting a relationship. Does the intent transfer, or just my warm fuzzies for them? Because unless I mentally articulate the intention, it could be a source of miscommunication, if not really a lie.
Memory - now this is a fun one! Memories might consist of thoughts and feelings, but in reality they are neither. Do others have access to only what I am remembering at the moment, or does everyone within telepathic range share a collective memory? But I'm digressing from the question of lying.
Based on what you describe, no, I don't think it's possible to intentionally deceive someone, which is usually via misinformation. Moreover, the social dynamic would be extremely different from ours. I don't think there would be cause for intentional communication - if everyone knows X, you can't articulate X any better to them. It would be redundant. I doubt there would be language or words - just a flow of abstract concepts. I don't think this society could even be aware of the concept of lying or deception, which makes an extremely interesting premise in itself.