Sure
Dim X, Y
X =DLookUp("ProjectUnitNoID","ProjectMaterialsT","ProjectItemID=" & [ProjectMaterialID])
Y =DLookUp("TextField","OtherTable","ProjectUnitNoID=" & X)

I can only do it with code?  Would it placed in "After Update"?

Put it in any relevant event, if you need the value after you enter a value somewhere else then afterupdate is fine. The on current event of the form is probably good too.

Or you could put it in a query, base the form on it.
Make an expression
ProjUnit: DLookUp("ProjectUnitNoID","ProjectMaterialsT","ProjectItemID=" & [ProjectMaterialID])

Then make second expression
TextField: DLookUp("TextField","OtherTable","ProjectUnitNoID=" & ProjUnit)

Adam

One more question

Dim X, Y (As what?) Integer?
X =DLookUp("ProjectUnitNoID","ProjectMaterialsT","ProjectItemID=" & [ProjectMaterialID])
Y =DLookUp("TextField","OtherTable","ProjectUnitNoID=" & X)

In this case you dont have to declare it, them being type variant is fine with no as choice. But you could do integer

X and Y can't be integer (or string) because that would cause a run-time error if DLookup returned Null.  X and Y must be variant to avoid that.  Dim X is the same as Dim X As Variant.  If you must declare them with a type, use the Nz() function to handle possible Null value.