What to include in random structure? lmer

Should we still have trial number in the linear mixed effects model even if the item order is randomized not only for each participant but each session? I included participants as a random effect but not sure about whether item should also be included.

Session 1

Participant A                  Participant B

Item A                          Item C
Item B                          Item A
Item C                          Item B
Item D                          Item D

Session 2

Participant A                  Participant B

Item E                          Item H
Item G                          Item G
Item F                          Item F
Item H                          Item E