I have developed a macro based on the above code, aligning multiple dimension lines. Hope this help.
The sequence is:
1) Scan and select multiple dimension lines
2) Click on the macro
3) Select base dimension
But sometimes an error occurs on line 19, I don't understand much about it, but in short it still works.

Option Explicit
Sub AlignDimension2()
Dim Dim1 As LinearGeneralDimension
Set Dim1 = ThisApplication.CommandManager.Pick(kDrawingDimensionFilter, "Select Base Dimension: ")
Dim oDoc As DrawingDocument
Set oDoc = ThisApplication.ActiveDocument
Dim oSelectSet As SelectSet
Set oSelectSet = oDoc.SelectSet
Dim oItem As Object
Dim oPoint As Point2d
For Each oItem In oSelectSet
Set oPoint = oItem.Text.Origin.Copy
If Dim1.DimensionLine.Direction.x <> 0 Or Dim1.DimensionType = kHorizontalDimensionType Then
oPoint.y = Dim1.Text.Origin.y
Else
oPoint.x = Dim1.Text.Origin.x
End If
oItem.Text.Origin = oPoint
Next oItem
oSelectSet.Clear
End Sub