I just got out my DS and tested with Lameboy v0.11 since that's the latest version I have on my card. My test game was Azure Dreams, which is an interesting game in that it works in regular GB mode but also has a Super Gameboy border as well as full GBC colors. I could get it working in all three modes in Lameboy by changing the two appropriate settings before launching the game. Here's what I got.
SGB off and GBC "never": no border, black and white
SGB on and GBC "never" or "as needed": SGB border with limited 4-color palette (though I don't know if it's the standard SGB palette #1 or if it's a custom one included in the game)
SGB on/off and GBC "always": no border, full GBC colors
The only combination I could not get was to have the SGB border with GBC colors, which is an option I don't believe Lameboy supports (or if it does, it only does so in v0.12).
So I'm not entirely sure what the issue is for you. If it helps, all of my games end in .gbc and not .gb. The only other game I tested was Pokemon Red, but that too has a custom SGB border. Perhaps SGB mode only applies on Lameboy if the game was designed for it? I don't know if Star Trek was or not. It's likely that IGN took that screenshot from a GBC, which applies its own colors based on a hard list of games included on its BIOS. Lameboy does not emulate the GBC colorings of GB games in that way, because at the time when Lameboy was made, it was believed that the BIOS could not be dumped (it later was successfully dumped).
EDIT: According to http://en.wikipedia.org/wiki/List_of_Super_Game_Boy_games#S only "Star Trek Generations: Beyond the Nexus" had SGB enhancements. As there was at least one other Gameboy Star Trek game, I don't know if this was the game you tried.