No, I doubt people would follow you into parking lots just because you have a LV. Thieves target people who look like they don't know what they are doing, distracted or obviously not from the area. Plus, I'm sure you would be keeping a close eye on the bag. That awareness makes you less of a target.
As for family members, it depends on whether "money" is a big deal for them. If money is tight and they know LV bags, they may feel uncomfortable. If you don't flaunt it, I'm sure you'll be fine.
LV monogrammed bags are quite flashy so people will probably stare if they are uncommon where you live/frequent, so you will definitely get more attention. The amount of attention totally depends on the area you're in. Less well off communities you may receive more negative attention, middle to upper-middle class communities you may receive more complements, and super wealthy areas, no one will bat an eye.
My opinion, based on observations.