Is it okay to tear open some lavender tulsi herbal tea bags?
Quite often teas go through a fermentation process that changes and intensifies the flavors. Herbal teas often mix a dried but non-fermented main aromatic like lavender with some sort of green or black tea which is fermented. A good example of this is mint tea, which is generally dried mint mixed with green tea. I wouldn't use mint tea as a substitute for fresh mint, it's never going to work the same.
Ripping open a tea bag and sprinkling it on a tuna salad isn't likely to win you any awards when people start crunching into bitter dried leaves. To be honest it would be hard to think of a more effective way to ruin it. Just add some fresh basil leaves instead, or ask around where you can gather some fresh lavender, it grows all over the place.
You can certainly try it. I don't know if the tulsi flavor will be what you want or not, though.
I also don't think I've ever heard of eggplant niçoise with lavender (and couldn't find a recipe with it) so it's probably also fine without it if you don't think the flavor's going to be what you want.