It’s a brilliant quote , but its also one with a lot of psychological ambiguity , Lawrence’s book is full of nuance which makes a lot of his writing have layers of meaning.
It’s a bit like Hemmingway’s concept of the “Iceberg” in the sense that a statement essentially includes a great deal of omission like when you only see the top of an Iceberg above the surface of the water and not the true size of it underneath the sea.
So in terms of “the dreamers of the day” , it is a nuetral and morally ambiguous statement. Lawrence is on the one hand suggesting that it is a character trait with positive qualities in the sense of self actualization but also he uses the word “dangerous” to hint that there are drawbacks to being this kind of dreamer.
Because in a certain sense he is implying that this trait can lead to becoming like a Frankenstein’s monster that wanders/ sleepwalks through life without really being awake and possesing an almost solipsistic view of achieving dreams without the awareness that this can be quite selfish in the way that it harm others and may become self destructive.
A lot of this nuance comes from his life story , he went out to Arabia to follow his dreams of becoming an archeologist but then due to WW1 was conscripted into fighting against the Ottoman empire in the Middle East. He achieved the dream of becoming a famous wartime hero and guerilla leader and leading the Arabs to a brief period of independence. But he then felt crushed and a sense of agonizing existential guilt and depression when the Western empires of France and Britain stepped in and co-opted and subverted this independence to serve their own imperialistic ambitions in the Middle East. In a sense he was recognizing how simultaneously liberating and destructive his tendency of being a dreamer really was , how his dreaming had unwittingly led to the betrayal of the Arab peoples.
I’ve made this into a little bit of lecture , hahaha , but I just thought the context was necessary to add.