You can use AcadBlockreference.GetDynamicBlockProperties() method to get an array of dynamic properties of a dynamic block reference. Then you loop through the properties to find your target property (by its PropertyName, usually). If it is an lookup parameter, you can then get the lookup list from the dynamic property's AllowedValues.
Here is sample code working against a dynamic block, which has a lookup parameter called "MyLookup", which has a few values defined in the lookup list:
Option Explicit
Public Sub SetBlock()
Dim ent As AcadEntity
Dim pt As Variant
Dim blk As AcadBlockReference
Dim props As Variant
Dim i As Integer
Dim j As Integer
Dim prop As AcadDynamicBlockReferenceProperty
ThisDrawing.Utility.GetEntity ent, pt, vbCr & "Select a dynamic block:"
If ent Is Nothing Then Exit Sub
If TypeOf ent Is AcadBlockReference Then
Set blk = ent
If blk.IsDynamicBlock Then
props = blk.GetDynamicBlockProperties
For i = 0 To UBound(props)
Set prop = props(i)
''MsgBox prop.PropertyName
If UCase(prop.PropertyName) = "MYLOOKUP" Then
For j = 0 To UBound(prop.AllowedValues)
MsgBox "Lookup Value " & (j + 1) & " = " & CStr(prop.AllowedValues(j))
Next
End If
Next
End If
End If
End Sub