forgot to record replenishment testing and do not feel like re-doing it, but you can either take my word for it or check for yourself.
Lynchpin does not function with replenishment sources such as kills, feats or abilities, or blessings. It does not provide replenishment bonuses for your squad members in coherency regarding kills, replenishment restoring feats or abilities, or blesssings. It only provides regeneration bonus for yourself and nobody else for out of melee combat toughness regeneration. If this is intended function of the feat, the description needs to be rewritten as it is confusing and can be misinterpreted several ways.
Die-Hard does work with feat and kill replenishment source, but does not work with blessings and does not impact regeneration. It can be considered working as described, but description that explains blessings do not work with this feat would be nice to have to prevent confusion, if the function is intentional.