I think I've read the first five books of the Wheel of Time series, but it was a long time ago. I started re-reading the first one recently. Moiraine has mentioned several times about being afraid, but Lan hasn't. He seems unshakable in his courage. Does he ever mention being afraid or fearful of anything in the course of the series?
To the best of my knowledge, there is exactly one instance in the Wheel of Time series of Lan explicitly acknowledging experiencing fear. This occurs in Chapter 16 of New Spring when he learns of Edeyn's plans to coerce him into raising the Golden Crane and lead men in reclaiming Malkier from the Blight. Lan is so unsettled by this news that he actually resorts to the Flame and Void to regain his mental equilibrium:
Seating himself cross-legged on a bale of straw, he formed the image of a flame in his mind and fed emotion into it, hate, fear, everything, every scrap, until it seemed that he floated in emptiness.
This is not stated specifically in reference to Lan, but apparently when Lanfear and Moiraine fought in Book 5 at the docks in Cairhien and went through the door frame ter'angreal, the effect on him was the same as if Moiraine had been killed. Warders whose Aes Sedai is killed become suicidal. This being the case, what would he be afraid of? Apparently with Lan, the only thing that saves him from what is described by the Aes Sedai as a "death wish" is the fact that Moiraine's Warder bond apparently included Myrelle Berengari, a Green who was close friends with her & Siuan, in a way that passed the bond to her if anything happened to Moiraine. Also, Egwene sent him a mission to protect Nyneave, which he certainly couldn't do if he got himself killed. Incidentally, Myrelle herself was known as one of the only sisters in living memory who could save Warders whose Aes Sedai died. (A Crown of Swords, Chapter 12)
I don't remember Lan ever showing fear for his own life or safety (and I re-read the entire series in the past two years, so it's relatively fresh in my memory), but I think he did express fear for Nynaeve safety. I've have to add references later (after my Kindle is re-charged).
You should change the title of your question, since from the body of the question it seems you ask only about a specific Warder - Lan - and not about Warders in general. There are plenty of examples of other Warders showing/admitting fear (Birgitte is the first one that comes to mind).