How do I keep cake from collapsing when adding lemon juice?

Does the batter type used rely on gluten development? Acids and enzymes from very concentrated fruit juices can weaken gluten - if it would be strong enough to tenderize meat (denature protein), it is not unlikely to break down or influence (even already developed) gluten (which is a protein).

Using a "stronger" flour than normally recommended for cakes, or adding extra gluten, or adding an additional binder could help.

I think your fat-to-flour ratio for that kind of flour might be too high. Cake flour can't handle a lot of fat. As another answer suggested, try a higher protein flour--start with all-purpose (AP) flour and, if that isn't enough, use bread flour but remember to barely stir it together or you will make a mess. I would mix everything together except the flour first, then carefully stir it in.

I read that adding extra baking soda, like a teaspoon, to the recipe will help counter the effect of the acidic acid on your leaving agent. But, in my case, I zested just one lemon and added the juice of half a lemon, to brighten the flavor. you may need to add a whole tablespoon in your case?

I think the issue with this recipe is simply too many lemons! You were blaming the acidity of the lemons for your issue: this explains the problems at least partially. This blog post bakes cakes with different amount of acid and explains the results. In summary, excess acidity will inhibit browning and impede rising. While adding baking soda can neutralize the cake, too much simply tastes bad.

Lemon bring a few other properties to the mix. As one of the comments mentions, lemon juice is mostly water. The excess moisture will leave your cake with less structural integrity; it may collapse. You could possibly fix this by adding more flour or starch, but it sounds difficult.

If you are not attached to your recipe, I recommend you just use a battle-tested and well-reviewed lemon cake recipe. The lemon bliss cake from King Arthur Flour looks like a good candidate. To avoid the issues caused by lemon juice, they use other techniques to incorporate lemon flavor:

• Lemon zest: the zest of a lemon has a ton of flavor but no acidity or moisture.
• Lemon oil (optional): much like zest, adds flavor without changing the chemistry of the cake.
• Glaze: a lemon juice-spiked glaze is applied after the cake is baked. This way it does not effect the baking process, but adds lemon flavor and moisture.
• Icing: after the glaze, a lemon juice icing adds even more lemon flavor.

But if you really wanted to modify the recipe you gave above, you can still try to learn from the lessons in the KAF recipe. You can use less juice and more zest, you could add a glaze, you could use lemon oil. Anything to remove excess lemon juice from your cake will likely improve the texture. Also adding 1/4 tsp of baking soda could counteract some of the acidity.