Hi David.

Seems quite simple, I would manage this by using isna() as a test, so if your first condition is false it stops.
Condition 1 does the desk exist
Condition 2 does the service line match.

=IF(ISNA(VLOOKUP(E12,'[Copy of Asset_movm_form.xlsx]Asset movement details'!$H$6:$I$27,1,FALSE))=TRUE,"No Desk",IF(VLOOKUP(E12,'[Copy of Asset_movm_form.xlsx]Asset movement details'!$H$6:$I$27,2,FALSE)=E10,VLOOKUP(E12,'[Copy of Asset_movm_form.xlsx]Asset movement details'!$H$6:$M$27,6,FALSE),"Fail"))

Clearly you can change bits and pieces to suit.

Hope it helps
Matthew