What is the Erso family’s relationship with the Force?

Question

There are some interesting but tenuous connections between scenes with the Erso family and the Force, not limited to the following:

• Galen Erso plays a critical role in the construction of the first Death Star, which is powered by kyber crystals-- they are also the power source for lightsabers. I acknowledge the distant potential relationship here, but considering Galen's complicated relationship with the Empire, I think it's reasonable to believe there is a connection here.
• Lyra Erso tells her daughter to "trust the Force" prior to their separation, in addition to giving her a necklace with a crystal that may or may not be a kyber crystal.

What role does the Force play in their lives? What is their relationship with the Force?

Answer 1

Lyra might be considered a non-Jedi believer in the Force.

Jyn had nursed herself to sleep, and Lyra could hear Galen and the others talking in the main cabin, glad not to be a part of the conversation. For her, governments of any stripe would have their constituents believe that they were attempting to remove chaos from the galaxy, that they were trying to make things perfect, when only the Force was perfect. For ordinary beings, life was a constant interplay between order and chaos, day and night, light and dark.

Her reverence for the Force had evolved from an enduring love of nature. Yes, she thought of herself as agile and strong and intuitive, but she understood that her skills were a far cry from those attributed to the Jedi. She did, however, embrace the Order’s philosophy of generosity, compassion, and peaceful resolution, and on many a far-flung world she had experienced moments in nature that could only be described as transcendent. It was certainly possible that those peak moments had their basis in belief and emotion, but that hardly mattered; even if she wasn’t able to use the Force, she could at least feel it, and she was content with that.

_{Catalyst: A Rogue One Novel}

We’ve seen these before, from some among the Lasat (who call it the Ashla), to the Church of the Force from The Force Awakens.

Galen isn’t much of a believer, but becomes obsessed with kyber crystals. He sees the Force as simply another aspect of nature.

“The Force derives from nature,” Galen said somberly. “Against such chaos, even the Jedi are capable of accomplishing only so much.”

_{Catalyst: A Rogue One Novel}

He even hopes that the Force may one day be explained:

He nodded, as if assessing her words. “I’ll defer to the Order’s sound judgment. We’ll investigate with judicious care. But who knows, one day we may even get to the root of the Force itself.”

_{Catalyst: A Rogue One Novel}

That Lyra had a kyber crystal to give to Jyn can easily be attributed to Galen’s access to them during his research, and her own affinity for all things related to the Force.

Answer 2

This is referenced in the Star Wars: Rogue One - The Ultimate Visual Guide. In short, Lyra Erso has developed a spiritual connection to Jedi philosophy and may be a covert Jedi sympathiser.

Although Lyra has never met a Jedi Knight. she studied their history and philosophies, even when the Galactic Empire frowned upon such research. It is not known if she ever made contact with the rumoured Church of the Force movement reputed to be growing in the shadows of Coruscant, but she did at that time don the scarlet vestments of the sects native to Jedha - One of the last holy outposts of Force knowledge in the Galaxy.

The crystal necklace was indeed a khyber crystal. It has some Aurabesh writing on it, but it doesn't appear to have any meaning when translated into English (UT?N THN)

This small stone - a fragment of khyber crystal from Galen Erso's research - caught Lyra's eye as her family fled Coruscant. She took it to be a good omen and passed it to Jyn, who at the time didn't understand, but knew it was a gift nonetheless.