Ms Damari, 28, was taken hostage from Kibbutz Kfar Aza when Hamas gunmen stormed across Gaza’s border into Israel on 7 October last year, killing about 1,200 people and taking 251 others as hostages.
A total of 97 hostages remain unaccounted for.
Israel responded with a military campaign in Gaza, which has killed thousands in the Palestinian territory.
“This is a painful day for the Jewish community across this country and across the diaspora,” Lammy told reporters in his constituency.
“It is a day of deep reflection and pain thinking about 7 October, the worst attack on the Jewish community since the Holocaust,” he added.
Addressing a memorial event in London on Sunday, Ms Damari’s mother Mandy said that hostages released last November had told her they had had contact with Emily in captivity.
On Sunday, Sir Keir said the country must “unequivocally” stand with the Jewish community and described 7 October as the “darkest day in Jewish history since the Holocaust”.
“As a father, a husband, a son, a brother – meeting the families of those who lost their loved ones last week was unimaginable. Their grief and pain are ours, and it is shared in homes across the land,” Sir Keir said.