Lux has CC, poke, zoning, more damage (base and scaling both), and shields. What do you mean by "anti dive"? You've used the term several times without ever clarifying what you mean by that.
Here, I've worked it out, if you care to see what I mean.
Lux:
Snare (Q) damage: 50/100/150/200/250 base (maximum early-game: 100/200/300 base, 2 targets)
Cooldown: 13/12.5/12/11.5/11 seconds (maximum damage per second: 7.7/16/25 base, 2 targets)
Damage denial (W): 150/195/240/285/330 base (maximum early-game: 450/585/720 base, 3 targets—300/390/480 base, 2 targets)
Cooldown: 14/13/12/11/10 base (maximum denial per second: 32.14/45/60 base, 3 targets—21.43/30/40 base, 2 targets)
AoE (E) damage: 60/105/150/195/240 base (maximum early-game: 180/315/450 base, 3 targets—120/210/300 base, 2 targets)
Cooldown: 10 seconds (maximum damage per second: 18/31.5/45 base, 3 targets—12/21/30 base, 2 targets)
Ultimate damage: 300/400/500 base (maximum early-game: 900 base, 3 targets—600 base, 2 targets)
Cooldown: 80/65/50 seconds (maximum damage per second: 11.25 base, 3 targets—7.5 base, 2 targets)
Collected maximum damage, full burst at 6: 852.5 base (including passive), 2 targets with 25.22% MR.
Collected maximum damage denial at 6: 300
Damage quality at 6: 1152.5 base
Damage per second at 6: 33.8 (no passive) base, 2 targets with 25.22% MR—39 (1 passive proc per 10 seconds) base, 2 targets with 25.22% MR
Damage denial per second at 6: 21.43 base, 2 targets
Damage per second quality at 6: 60.43 base
Zyra:
Snare (E) damage: 60/95/130/165/200 base (maximum early-game: 180/285/390 base, 3 targets—120/190/260 base, 2 targets)
Cooldown: 12 seconds (maximum damage per second: 15/23.75/32.5 base, 3 targets—10/15.83/21.67 base, 2 targets)
AoE (Q) damage: 60/95/130/165/200 base (maximum early-game: 180/285/390 base, 3 targets—120/190/260 base, 2 targets)
Cooldown: 7/6.5/6/5.5/5 seconds (maximum damage per second: 25.71/43.85/65 base, 3 targets—17.14/29.23/43.3 base, 2 targets)
Ultimate damage: 180/265/350 base (maximum early-game: 540 base, 3 targets—360 base, 2 targets)
Cooldown: 130/120/110 seconds (maximum damage per second: 4.15 base, 3 targets—2.77 base, 2 targets)
Collected maximum damage, full burst at 6: 962.8 base (including 3 plants), 2 targets with 25.22% MR
Damage quality at 6: 962.8 base
Damage per second at 6: 58.0 base (assuming 1 plant attack every other second), 2 targets with 25.22% MR
Damage per second quality at 6: 58.0 base
Brand:
Stun (Q) damage: 80/110/140/170/200 base (maximum early-game: 80/110/140 base, 1 target)
Cooldown: 8/7.5/7/6.5/6 seconds (maximum damage per second: 10/14.67/23.3 base, 1 target)
AoE (W) damage: 75/120/165/210/255 base (maximum early-game: 225/360/495 base, 3 targets—150/240/330 base, 2 targets)
Cooldown: 10/9.5/9/8.5/8 seconds (maximum damage per second: 22.5/37.89/55 base, 3 targets—15/25.26/36.67 base, 2 targets)
Single target (E) damage: 70/90/110/130/150 base (maximum early-game: 210/270/330 base, 3 targets—140/180/220 base, 2 targets—70/90/110 base, 1 target)
Cooldown: 10/9/8/7/6 seconds (maximum damage per second: 21/30/41.25 base, 3 targets—14/20/27.5 base, 2 targets—7/10/13.75 base, 1 target)
Ultimate damage: 500/1000/1500 base (maximum early-game: 500 base, 2 targets)
Cooldown: 105/90/75 seconds (maximum damage per second: 4.76 base, 2 targets)
Collected maximum damage, full burst at 6 (W>E/Q>Q/E>R): 1026.88 base, 2 targets with 25.22% MR
Damage quality at 6: 1026.88 base
Damage per second at 6: 67 base (including full passive), 2 targets with 25.22% MR
Damage per second quality at 6: 67 base
Disregarding mana costs (none of these should be running out of mana in the support role), Lux has higher damage per second quality (damage + damage denial) than Zyra, but lower than Brand. Lux also has significantly higher burst potential/denial in an all-in.
Lux isn't meant to be a poke support, as much as Brand and Zyra. She keeps the two laners from taking damage until an all-in opportunity. She can still poke a significant amount, but it's clear here that her all-in is more powerful.
She has the utility required for being a support, and her early-game is not weakened by "low base damage" (as so many people are fond of saying). Just going off base damages, she is easily as strong as either of these supports. There is no reason to prefer Zyra or Brand over Lux.
Does this make sense?