Lysithea should very well survive it, so its not a problem. At worst you can use a shield and see if that helps or if it forces a more favorable target.
Your Dimitri clearly needs more defence. Give him a Aegis Shield and Duscur batallion = +16 defence. He is the tankiest out of 3 lords and in my playthrough he took basically no damage after timeskip (except that one time that Hilda killed him but thats just Hilda being Hilda).
The map is very anti-dimitri but its because its mage-heavy and he is bad against magic, which is fine because Ingrid is very good, or short of Ingrid your Byleth should be able to Retribution the shit out of any boltings / rush the artillery units. If getting in range of ballista's proves too difficult BL has Sacred Shield batallion.
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You can also whip out 5 HP talent on your Lysithea
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Oh and suffice to say you can also focus on getting a unit into a throne room to force her to switch in melee mode