“Faith is based on revelation, but a revelation that takes place each day.”
“Faith is based on revelation” – 
“Revelation” isn’t commonly used in Judaism to describe a feature of every-day life.
But in Torah and in “NaCh,” people are often said to “see G-d,” to “lift their eyes,” etc.
To “see G-d” is a revelation.
We all have “revelations.” We just don’t call them that.
“Revelation” comes from “reveal” – the “hidden” becomes known; “unveiled,” as it were.
G-d’s presence is always “with” us, always “in” us, but not always clear to us.
When it becomes “clear,” it’s “revealed.” We have a “revelation” of what was there all along.
Rabbi Lichtenstein is saying that “faith” – emunah – isn’t only an intellectual or emotional belief, based on hope or even tradition (although these have their value, too). It’s based on personal experience of G-d’s presence. It’s “revelation.” The Divine Presence, always with us and in us, becomes “unveiled” to us, as when Ya’akov says, “G-d was in this place and I didn’t know it.” (Ber./Gen. 28:16)
The midrash says “G-d’s Name is ‘Peace’.” (Vayikra/Lev. Rabbah 9:9). The “name” of a thing is its definition; it’s most perfect description; it’s “identity.” The midrash, then, is saying that our experience of G-d will be one of perfect Peace.
Each time in our lives that we have an experience of G-d, or of G-d’s peace, even if only for a moment, we’ve had an indisputable “revelation” of G-d’s Presence.
Thus, the “Duties of the Heart” says, ““Among the wordly advantages of trust [בטחון] are to be found: a heart at rest…” (Rabbi Bahya ibn Pakuda; Duties of the Heart; Feldheim; vol. 1, p. 291)
Faced with a problem, “belief” might tell us that G-d can “do anything,” leaving us with a positive idea, but an unquiet heart. If, at that moment, we truly “lift our eyes” and “see” with our hearts G-d’s supremacy over any problem or condition, let go of the problem, we turn from visible, material creation to its Source. At the same moment, we move from the finite, conscious level of our minds to the unchanging Infinite level. We transcend.
“When we give ourselves up to the contemplation of G-d, our soul takes us into a region beyond our present physical world…We transcend, we go beyond the limitation of finite thought, and we draw therefrom power, strength and wisdom …If we have been nervous, tense or worried, we can, in a few minutes, cause ourselves to become calm…It is a deliberate and conscious change from our daily thinking to a communication with the infinite, through our soul…It has been said that we can experience union with something larger than ourselves, a sense of oneness with the power beyond…in that union, we shall find our greatest contentment and peace. That union we make and can experience only through our soul.” (Schwartz, Charles and Bertie; Faith through Reason; National Women’s League of the United Synagogue of America; 1946; p. 28-9)
“…that takes place each day” –
Rabbi Lichtenstein adds to this that “faith” – emunah or bitachon – must be new each day. Otherwise, yesterday’s “revelation” is just today’s recollection; something we do habitually, without feeling, based on a memory. Perhaps that’s why Torah mandates sacrificial services morning and evening. We worship – “unveil” G-d to ourselves – at the conclusion of each day’s activity, and do the same again the following morning, at the commencement of the next day’s activity. Every true experience of G-d seems “new” to us.
How amazing to think of a future time when such an “unveiling” is an ongoing experience for all of us, at every moment of every day!
 Lichtenstein, Rabbi Morris; Jewish Science and Health; p. 137