BarLegend can't make spaced contours when contours number>11

makeContours[barLegend_BarLegend] /; (Length[barLegend] =!= 2) := barLegend

makeContours[barLegend_BarLegend] := 
 Module[{colorScheme = barLegend[[1]], contourCount = barLegend[[2]]},
  If[IntegerQ[contourCount] && contourCount > 11 && 
    DataPaclets`ColorDataDump`colorSchemeNameQ[colorScheme], 
   ToExpression[
    MakeBoxes[barLegend] /. 
      RasterBox[colors_, scale_] :> 
       RasterBox[List@*List @@@ ColorData[colorScheme] /@ Subdivide[contourCount], scale] /. 
      (InterpretationFunction :> _) -> (InterpretationFunction :> (# &))],
   barLegend]]

makeContours@BarLegend["LakeColors", #] & /@ Range[8, 20] // Row

Although there are hidden options to the underlying function (Charting`iBarLegend) that seem to address the required functionality, there does not seem to be any way to get the user-exposed function BarLegend to react to them. The following did not change the presentation of the test cases you provided, and neither did attempts to pass some promising-sounding options directly through BarLegend. For example the following did not change anything:

BarLegend["LakeColors", 12, "SmoothRange" -> False]

I suspect that there is no way to get the desired effect in current versions of Mathematica using straightforward options, though I could be wrong. And as Karsten's excellent answer shows, it is possible to force the issue by constructing the raster manually.

SetOptions[Charting`iBarLegend, ShowContours -> True]

{ColorFunctionScaling -> Automatic, ImageSize -> Automatic, 
 ImageSizeAction -> Automatic, RoundingRadius -> Automatic, 
 FrameStyle -> Automatic, Alignment -> Automatic, 
 Spacings -> Automatic, Scrollbars -> False, ScrollPosition -> {0, 0},
  Background -> Automatic, ContentPadding -> True, 
 DefaultLabelStyle -> {}, "Orientation" -> "Column", 
 Charting`AxesLabelRotate -> True, Charting`AxisAnnotation -> None, 
 Charting`AxisFactor -> None, Charting`AxisAppearance -> Automatic, 
 Charting`AxisLabel -> None, Charting`LabelSide -> Automatic, 
 Charting`PadLabels -> Automatic, Charting`RotateLabels -> False, 
 Charting`TickAnnotations -> None, Charting`TickSide -> Automatic, 
 Charting`TickLabels -> Automatic, Charting`TickLengths -> Automatic, 
 Charting`TickMarkers -> Automatic, Charting`TickWrappers -> None, 
 Charting`RotateTicks -> 0, AxesLabel -> None, AxesStyle -> Automatic,
  Frame -> True, FrameStyle -> Automatic, 
 LabelingFunction -> Automatic, Ticks -> Automatic, 
 TicksStyle -> Automatic, AspectRatio -> Automatic, 
 ScalingFunctions -> {Identity, Identity}, BaseStyle -> {}, 
 "LegendMethod" -> "Fixed", "Density" -> "Continuous", 
 "SmoothRange" -> True, "AxesPriority" -> Automatic, 
 "Sorting" -> True, "ContourMethod" -> "Graphics", 
 "RenderMode" -> Automatic, "LegendItemLayout" -> Automatic, 
 "PinningPoint" -> None, "StyledContours" -> None, 
 "ShowContours" -> True, PlotTheme -> "Mathematica"}

It's probably obvious to people with more experience than I, but since it took me a while to figure out:

If you want to modify Karsten's excellent answer above to produce horizontal BarLegends you need to take three inputs, transpose the matrix used in RasterBox, and add the LegendLayout->Row option to the function call:

makeContours[barLegend_BarLegend] /; (Length[barLegend] =!= 3) := barLegend

makeContours[barLegend_BarLegend] := 
Module[{colorScheme = barLegend[[1]], contourCount = barLegend[[2]]},
  If[IntegerQ[contourCount] && contourCount > 11 && 
    DataPaclets`ColorDataDump`colorSchemeNameQ[colorScheme], 
   ToExpression[
    MakeBoxes[barLegend] /. 
      RasterBox[colors_, scale_] :> 
       RasterBox[Transpose[List@*List @@@ 
      ColorData[colorScheme] /@ Subdivide[contourCount]], 
     scale] /. (InterpretationFunction :> _) -> \
    (InterpretationFunction :> (# &))], barLegend]]

 makeContours@BarLegend["LakeColors", #, LegendLayout -> "Row"] & /@ 
 Range[8, 20] // Row

One additional note. If in OS X you export one of these bar legends to pdf, the discrete color blocks will disappear and you'll be back to a smooth gradient. Frustrating! This is because of a bug in Mathematica's pdf export, described here along with the unfortunate solution: PDF exports of ArrayPlot's are fuzzy (OS X) .