How to break a heavy poke team's siege?

With that team, you should have won. Let's split up what you and they have:

Your Team:

• Gnar: Brutal Engage, Tanky, Much CC
• Rek'Sai: Sneak around with Ult, detect enemies in the area which might poke, good engage too, Average CC
• Swain: Teamfight God, almost unkillable, extremely tanky in extended fights, good CC
• Graves: Extremely huge burst, perfect for engages, no CC
• Braum: Tanky, can block projectiles, stun and a perfect ult for fights, Much CC

Enemy Team:

• Jayce: Strong Poke, average disengage, no CC
• Nidalee: Strong Poke, Heal, average tankiness, no CC
• Xerath: Stupid strong poke, average CC
• Caitlyn: Average Poke, no CC
• Sona: Low heal, good CC, but extremely squishy

What do we notice first? They have neither any valuable disengage nor a lot of CC to lock you down. While you just have a brutal comps for teamfights and also a lot of CC to lock targets down. You also hat a lot of surprise engages with Rek'Sai and Gnar who could have jumpes over walls to flank the enemy. If Gnar or RekSai are inside, Braum could have jumped to them and Ulted himself, creating a 3 - 4 second CC chain if the spells are placed correctly. Taking out Caitlyn or Xerath in one of those fights would have turned the tides completely in your favor.

There are just 3 reasons why you've lost this:

• You lost the game too early and the enemy had too much of a lead
• Gnar/Rek'Sai didn't have the balls to engage
• The enemy was simply much more skilled than you were

It is easiest to explain with the supports.

You have melee supports that have to all in and kill enemy from 100 -> 0 (leona, braum)

You have supports that do a lot of ranged poke damage. (Zyra, morgana, lulu)

You have supports that have sustain and some poke in their kit (sona, soraka)

Kill beats Sustain beats Poke beats Kill

sustain beats poke: The sustain lane has weaker poke damage than the poke supports, but after this poke it can heal themselves up, staying at full hp while the poke lane is damage.

poke beats kill: poke lane has high damage and also does constantly damage to the kill lane supports. This mean that these kill lane melee supports are often around 50% health and will be killed if the engage.

kill beats sustain: sustain heroes usually lack the escape skill and are quite bad at trading, the kill support jumps on a sustain hero and locks him for an easy kill

since your team lacks sustain - it will be quite hard for you to take on a poking team