As in this question, if you begin "leolam yehey" at the beginning of shacharit near the end of the time for reciting shema, and you may not otherwise recite it in time, you are supposed to recite a full shema there at "leolam yehey".
In such a case, should you cover your eyes when you say shema in "leolam yehey..." in the beginning of shacharit?
According to Ben Ish Hai I Miqes (S"Q 7)
כשיגיע לק"ש קודם פרשת התמיד יזהר לומר פסוקים שמע ישראל ובשכמל"ו בכונה גדולה כמו ק"ש דיוצר, הן בסגירות עיניו
When one reaches the Qeriat Shema prior to Parashat HaTamid he should be scrupulous to say Shema and Baruch Shem with great intention like the Keriat Shema of Yoser (Ohr). Including closing the eyes...
As the Kitzur Shulchan Aruch implies in 17:3, covering one's eyes is done to help one concentrate.
Since in "leolam yehey" one usually is not fulfulling the Mitzva of saying Shma, there's no reason to cover one's eyes.
However, if one is saying the full Shma in "leolam yehey" due to time constraints, then one should have to cover one's eyes.
