I'm not an expert but skimmed the two documents that seemed most relevant. The mortality rate analysis of the study and how they derive the $1235 per life estimate from it. 

Two things that I noticed, which jlewars didn't mention yet:
[Again not an expert, so don't make any conclusions based on what I write here.]

• They estimate that their intervention results in "9.2 additional baby lives saved for every 1000 live births". This point estimate comes with a pretty large confidence interval  (95% CI: 0.9,17.6). So the $1235 per life saved should possibly be read as similarly uncertain.
• They note that "The NMR [Neonatal Mortality Rate] seen in our study is much higher than the national average and most likely because participants were recruited from tertiary care facilities and have Special Newborn Care Unit beds.". If I understand it correctly, the intervention in the study was conducted on a quite specific vulnerable subgroup. With Quasi-Experiments and RCTs the external validity (how well does the intervention work on a different study group, in a different region?) is questionable, especially whenever there aren't many additional studies being done in different contexts. 
  So, even if Noora Health's intervention was as effective as they suggest, the question of how well the intervention is scaled for mothers in other contexts is a separate question. (However, if they use additional funding in a similar context this is not such a big problem.)

This isn't my area of expertise, but a quick review suggests that they are basing the numbers on a single study, which wasn't an RCT - it was a 'before and after' with an attempt at a control group.

That doesn't mean it isn't worth looking into, for sure, but I could equally believe that the extra rigour of an RCT could move the cost per lives saved from ~$1200 to a number several times higher than that.

It still merits furthers investigation though.