I'm sure your familiar with the effect of how the taste of fresh lemon juice practically disappears when it's cooked or baked. Most of what we think of as lemon taste isn't detected by our taste buds but by the nerves of our palate. Lemon juice alone doesn't add enough to the taste of cheesecake. Most of it's palate flavor and aroma are in highly volatile oils which cook off. However it does add some acid, which balances the sugar, and amps the cheese's tang quite a bit. Here, tang = sour, and that is detected with the tongue. So, the short answer is that lemon juice makes a plaint cheesecake taste more like plain cheesecake. And that's a very good thing.
If you want a lemony cheesecake, what really packs a punch is lemon zest. More so since the microplane did so much to improve the taste/bitterness ratio of freshly home-harvested zest.
It might add a little nuance to consider that if you bake with all juice and no zest, you'll lose almost all the lemon character you taste in the uncooked batter, but get a very "cheesy" cheesecake. On the other hand, if you bake with all zest and no juice, you'll get plenty of fruit but it will tend to be bitter and to overwhelm.
I suppose that there are some cheesecakes I'd try to bake without using vanilla, but not many. Vanilla does a lot to smooth out other flavors even in amounts too small to make its presence known. By way of example, chocolate is much better with than without vanilla, so too with nearly all fruits.
When balanced with most citrus in amounts where both flavors can assert themselves, it creates a wondefurl "dreamsicle" effect. It's also a great way to deal with zest's tendency towards bitterness. And okay, I'll be specific about "most citrus." I'm talking zest from orange, lemon, lime, orange/lemon, lemon/lime, and orange/lemon/lime/grapefruit (wonderful!).
You or your friend might try that all zest combination along with a few tablespoons of a flavorful dark rum like Brugal or Captain Morgan's to make a "Navy Grog" cheesecake. Just an incredible follow up to barbecue.
Food for thought,
PS. If you're going to copy and paste this post in whole or in part, you have my permission to do so as long as you credit me, Boar D. Laze. I'd consider it a kindness if you would also mention my eventually forthcoming book, COOK FOOD GOOD: American Cooking and Tehcnique for Beginners and Intermediates.