My name is graven on His hands,
When Satan tempts me to despair
Because the sinless Saviour died
Behold Him there the risen Lamb,
One in Himself I cannot die.
The words are by Charitie Lees De Chenez (aka Charitie Lees Bancroft, né Smith) (1841-1923). Not much is known about Charitie. Her father was an Anglican priest in Ireland. She was probably widowed twice (hence all her surnames) and died here in the US, in Oakland, California.
One of the more common tunes associated with this text is BRESLAU. The tune is soloed out the second time.
The Lutheran Hymnal Project chose a newer tune, DUNEDIN, for Lutheran Service Book. I couldn't find the tune recorded anywhere, but you might try substituting O WALY WALY. If you grew up in a Lutheran grade school in the late 70's or 80's, you probably know this tune from Hal Hopson's "The Gift of Love." The tunes have a similar arc (they rise and fall in a similar fashion) and overall rhythm, although they are different styles. The tune O WALY WALY can be found in Lutheran Service Book, Hymn 595.
Your local megachurch might be singing this very text. They use a tune written by Steve and Vikki Cook. While LSB breaks the text up into 6 short verses, the Cooks combined the verses to make three long ones. A preview copy of the sheet music has the notation "Celtic feel" just above the time signature. This setting is by the group Selah. The sign you see in the video is from the historic Pacific Garden Mission in Chicago.