If the H in your LiH is deuterium, absorbing neutrons would be OK, because that makes tritium. Not quite as much as lithium absorbing them, but better than anything else.
Hundreds of tons of deuterium in your thousands of tons of terrifyingly inflammable LiD would be expensive. But if we balk at expense, we won't get fusion power.
Most of us do, in fact, balk at expense, for reasons. But the topic here is what would be needed for fusion to be made to work at all. $2B worth of deuterium to help breed tritium is not much for a $100B fusion plant.
Extracting your few grams of tritium every day from a thousand tons of LiD may be called somebody else's problem.
