I think part of the lead engineer's job is to foster trust. But garnering this feedback by asking the right questions is just as important. Even if it means asking difficult questions until answered.
If a team struggles with meaningful retrospectives, it might be because they don't see the value in them. When that's the case people can end up thinking "it's just another meeting", "just let me code". Or it might be because the trust isn't there, even though it might seem like it is. Exposing problems (of whatever nature), tends to end up involving management at some point, and I've noticed over the years that many engineers have a strange fear of management. You can't have a meaningful discussion about problems if you don't trust everyone involved, including management.
- Create a list of topics for your team to complain about at the retro. eg. Bugs, communication, management, programming practices, meetings... This should help stir some memories and emotions.
- Insist that each person give at least one piece of feedback. If someone is not willing to give feedback, make a silly suggestion for them. For example, in our last retro, a member was on holidays for 2/3rds of the sprint, and said he didn't have any 'good' feedback to give. I jokingly suggested that he was glad his holidays were over and he was able to be back at work with his team. A bit of humour helps break the ice. Any feedback, no matter how silly, is better than none at all.
- Take notes of any negative feedback during the sprint. If the retro lacks engagement, bring up one of these topics as a discussion point. People are forgetful - they may need some prompting!
- Take note of things you see need improving (use that 80/20 analysis). Bring these up as discussion points at the retro.
Remember, you are there to facilitate the team. But that doesn't mean you don't get involved. Lead the discussion when it runs dry, and don't be afraid to make suggestions. Show that you are passionate about improving the team and this will leak into the team 'culture' (that dreaded term!).
When I get at work a message like:
"VP XXX is very interested in your feedback, it would be great if you spend 15 minutes and fill the form". I delete the email.
"Very interested in your feedback" and mass email do not work well. In addition I do not feel that my feedback given in this way will affect anything.
I do not think that it is your problem. You say that it is not a matter of trust, but I am 100% sure that it is.
I give honest feedback at 1-1 meetings.
By the way, did you read https://www.goodreads.com/book/show/52283963-the-mom-test
and
https://www.goodreads.com/book/show/1317946.Managing_Humans
? It could help :)
Another common problem I see is senior people cutting off junior people or "correcting" them for political reasons. This is disastrous and makes the junior people stop talking real quick. When you're punished for making yourself vulnerable, you're going to stop making yourself vulnerable. It's a huge loss because junior people often see things with clearer eyes and can be a gold mine for an observant senior person.
The good news is that even dysfunctional teams can be turned around. You just have to stomp out bad behaviors and start up some virtuous cycles. A challenge but not impossible.