Yeah, Lemmix requires you to specify essentially a new graphics style for each special graphics you want to use.
Here's an example of how Lemmix specifies a style for DOS Lemming's VGASPEC0 in its LemmixStyles.ini file:
[DosOrig_5]
GraphicSetClass=TBaseDosGraphicSet
BrickColor=4291854368
GraphicExtFile=VGASPEC0.DAT
GraphicFile=VGAGR0.DAT
GraphicSetArchive=
GraphicSetId=0
GraphicSetIdExt=1
GraphicSetName=Spec0
MetaInfoFile=GROUND0O.DAT
It's similar to the normal styles, the main difference for VGASPEC is the additional specification of a GraphicExtFile and a GraphicSetIdExt. The GraphicExtFile specifies the filename of the file to use for the VGASPEC graphics. The directory is already specified as part of the CommonPath property in the [style_N] section that describes the DosOrig style (for Lemmix's "DOS Original Lemmings" style, see section [style_0] where it specifies the CommonPath).
The GraphicSetId and GraphicSetIdExt together identifies the criteria for using this style. In other words, when you open a level file and you select to use the DosOrig style, if the level's LVL data specifies 0 for the normal graphics set and 1 for the extended graphics set, then Lemmix will use this Spec0 style specified in this section.
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I'm assuming that you've created a "Sega Genesis/Megadrive" style as I've instructed Lemmix users to do earlier in this thread. In that case, you would want to add the following new sections:
[Genesis_5]
GraphicSetClass=TBaseDosGraphicSet
BrickColor=4291854368
GraphicExtFile=VGASPEC4.DAT
GraphicFile=VGAGR0.DAT
GraphicSetArchive=
GraphicSetId=0
GraphicSetIdExt=5
GraphicSetName=Beast
MetaInfoFile=GROUND0G.DAT
[Genesis_6]
GraphicSetClass=TBaseDosGraphicSet
BrickColor=4291854368
GraphicExtFile=VGASPEC5.DAT
GraphicFile=VGAGR0.DAT
GraphicSetArchive=
GraphicSetId=0
GraphicSetIdExt=6
GraphicSetName=Menace
MetaInfoFile=GROUND0G.DAT
[Genesis_7]
GraphicSetClass=TBaseDosGraphicSet
BrickColor=4291854368
GraphicExtFile=VGASPEC6.DAT
GraphicFile=VGAGR0.DAT
GraphicSetArchive=
GraphicSetId=0
GraphicSetIdExt=7
GraphicSetName=BeastII
MetaInfoFile=GROUND0G.DAT
[Genesis_8]
GraphicSetClass=TBaseDosGraphicSet
BrickColor=4289761296
GraphicExtFile=VGASPEC7.DAT
GraphicFile=VGAGR0.DAT
GraphicSetArchive=
GraphicSetId=0
GraphicSetIdExt=8
GraphicSetName=Awesome
MetaInfoFile=GROUND0G.DAT
[Genesis_9]
GraphicSetClass=TBaseDosGraphicSet
BrickColor=4291854368
GraphicExtFile=VGASPEC8.DAT
GraphicFile=VGAGR0.DAT
GraphicSetArchive=
GraphicSetId=0
GraphicSetIdExt=9
GraphicSetName=SunsoftSpecial
MetaInfoFile=GROUND0G.DAT
(Replace GROUND0G.DAT with GROUND0H.dat if you're using the "H" version of the ground files.) You'll also need to place the Genesis VGASPECx files into the same CommonPath directory you set in your LemmixStyles.ini for the Genesis style.
If you want to use Lemmix's "DOS Original Lemmings" style instead for playing the Genesis levels, simply add the above sections to LemmixStyles.ini but rename the section as [DOSOrig_N], where N starts off from 1 + the last number used for the existing "DOSOrig_N" sections in the file. And make sure to place the Genesis VGASPECx files into DOSOrig's CommonPath directory.