Regarding Lumosity.

The improvements one attains doing the program are not necessarily due to brain healing. Many of them are due to expanding the skills sets from previous low levels. It is like learning speed reading. You can be a competent reader but a speed reading course can develop undeveloped reading skills. Just like learning new balance skills or typing skills. Many have grossly under-developed observation skills. These exercises can cause great improvements.

It is only when the metrics are normed for age, education, etc. that they start to show improvements of skills lost due to injury.

Lumosity is just starting a research study with the VA regarding brain injury subjects.

This does not mean Lumosity is not worth the expense and effort. You may be able to develop skills that can help you work around skills that have been lost due to injury. Just be cautious you don't cause fatigue thus slowing organic recovery.