I don't have any of those characters so I don't know them that well, but I can give you basic guidelines.
The skills you give depends on how you want your team to work together. Takumi, Lyn and Cordelia are all strong offensive characters, but aren't particularly tanky. So your choices are to either help make one or two of those characters more tanky so that you have someone to put out as bait near the start of the fight (and possibly survive long enough for you to heal them), or add something to enhance the existing strengths of your characters.
For example, Vantage may be a good choice on Lyn because she naturally functions very well at lower HP thanks to some buffs kicking in at lower health. Vantage would mean that she has a chance of killing people that attack her when she's at lower health, which would make her harder to kill.
Vantage is also a good choice on Takumi for the same reason, though Takumi is becoming less common these days because people have counters to him.
Desperation is the offensive cousin of Vantage, which lets people attack twice in a row when they're lower HP, which may prevent enemy units from counterattacking and dealing damage to your unit before they die (assuming your unit can kill the target unit in two hits).
Cordelia has a Brave Lance iirc, which makes her strong for attacking but not as good at taking hits herself. I don't know her B skill, but if you are willing to give it up, she might benefit from Drag Back. That lets her move back one square after attacking, which may help take her someplace safer after she attacks.
Fury may be good for any of your three attackers, though keep in mind that it makes units stronger but also more fragile in the long run as they lose health (though you could heal them back with Lachesis).
For your C slot skills, I like using the skills that give adjacent units buffs at the start of a turn. These are easy to use because you can position your units in certain ways to benefit from the buffs. Attack buffs may help characters oneshot their targets. Speed buffs may help them double attack or avoid getting double attacked by others. Defense and res may make them tankier.
I don't have Lachesis and I'm not too familiar with her, so I can't help you there.