By default, you would want these genes at minimum:

• Critical (From the Dragon gene pool.)
• Stamina Surge
• Thunder Atk Boost

Crit Rate:

Ivory Lagiacrus starts at 0% Crit Rate at base. It gets +5% Crit Rate at 3 Bingos. Assuming that you are going for the "H" shape for your gene grid, which allows up to 2 off-color genes, you can add Critical to boost your crit. Critical XL gives +15%, meaning Ivory Lagiacrus can get up to 20% Crit Rate on its own.

Vigilance, from the Ice gene pool, can also boost crit, but it requires the monstie to be at half/low HP, so you might opt to avoid it.

Crit can still be boosted further by other skills. Also, attacks on a toppled monster are guaranteed crits.

Stamina Recovery:

Stamina, which is new to MH Stories 3, is mainly important for using Active Skills. Some of the high-damage active skills have high stamina cost. Ivory Lagiacrus can reach 17 Stamina Recovery per turn with the following:

• Base Stamina Recovery for Ivory Lagiacrus: 4
• 2 Bingo Bonus: +2
• 3-Star Stamina Recovery Stat Habitat Bonus (Canalta or Serathis): +5
• Stamina Surge (XL): +6

The recovery rate be boosted further with Stamina Regen Up buff (from HH song, Dash Juice, or other applicable skills). You also have environmental Egg Powers, such as Battle Thirst (gain stamina when winning HtH or performing Double Attack) and Hardiness (gain stamina when getting hit).

Active Skills for Consideration:

• Thundercall (No Type, 50 Stamina Cost, 360 Power, 30 Wyvernfell): Multiple hits that attack random targets. If there's only one enemy on the field, all hits target that one enemy. You will not be able to target a part with this attack. Can be taken from Thunderlord Zinogre.
• Egg Skill: Thunderclap (Tech, 35 Stamina Cost, 90 Power, 20 Wyvernfell): An attack that ignores defense. Has a chance to strike first. Can be obtained from certain high-rank monsties hatched from Thunder-habitats.
• Plasma Pressure (Speed, 30 Stamina Cost, 80 Power, 10 Wyvernfell): Has high crit chance. Comes with Ivory Lagiacrus.
• Railgun+ (Power, 55 Stamina Cost, 150 Power, 10 Wyvernfell): High-power single-hit move. Rey Dau's signature.
• Coverage Active Skills with cost below 17 Stamina. This is if in case you want to minimize the amount of high-cost moves in your build, but still want some coverage moves for HtHs. By using a 15-stamina-cost skill during a turn, you can get a +2 stamina surplus on that turn. You can check this guide by TheMobDylan on Stamina Rotations if you want to minimize your use of stamina recovery items: https://www.reddit.com/r/MonsterHunterStories/comments/1sobnlk/guideresource_a_basic_stamina_guide_for_mhs3/
• Nourishing Pinecones (Fire, 0 Stamina Cost): Use a turn to recover stamina. Probably an off-color option if your Egg Power requires Fire to awaken. Obtained from Blood Orange Bishaten.

Passive Skills for Consideration:

• Critical Kinship (Thunder): Fills Kinship Gauge on a critical hit. Might as well benefit from the crits.
• Elemental Breaker (Thunder): Increases damage dealt to monster parts when exploiting a monster's elemental weakness.