I asked my local tech community this question: What does the quote "Lead with Value" mean in regards to interviewing and "Lead with Values" mean in regards to being in a leadership role? The following is their answers.
I think of leading with value meaning you should be providing value to people. Like if you're trying to grow a brand and audience, do that by providing genuine value to people first. Don't focus directly on growth numbers.
“Lead with Values” in regard to leadership means treating other teammates with care and their best of interest. Should lead with positive vibes all the time. Create an environment such that teammates begin to expect outcomes from themselves.
In the case of a resume, if you have a statement “Did X with Y business impact” then you want to turn it around as “Y impact achieved by doing X” so that less technical people see the value first and if they stop reading halfway through due to technical knowledge then you at least gave them the important part. Technical people will dig in to see what details you listed and likely want to ask more questions if it is something really impressive.
Within social contract (in any business relationship especially) you do what you can to bring value to your partners. If this is a boss then help them to know the business impact of the thing that you are doing so that they can get the higher ups in support of the activity. If you ARE the boss then this means doing things like letting Joe Six-pack be involved in the DevOps work that needs to be done after he has expressed interest in DevOps during your one on one. You keep people interested in helping you by helping them.
In restaurant work I would do this for anybody that helped me to make money waiting tables. Keep the bartender happy and your drinks might be made faster, or at the very least, when you ask for something special or rushed then they will be more enthusiastic about doing so. Similar would go for my table cleaners, hosts, line cooks, and servers nearby. When people like you then they will not only be happier to help with the things that you ask them for, but also more likely to take it upon themselves to do something beneficial for you without your saying something. This also means that someone is going to be more helpful when you are standing shoulder to shoulder working together than they would be if you were standing over them shouting orders (see image)
Lead with Value to me means to show in the interview what value you create in the past that the interviewer would appreciate or find valuable for the company. If it is a website production shop then you should show past websites. If it is a Java shop, can you show applications made with Java. As in “Lead with Values” for leadership, this means to be an example of the idea worker that others want to emulate. The leader's values and ethics is shown in their actions.
Sharing your values is being authentic and people will choose to follow a leader if they believe they share that same values.
Lead with Value in an interview vs in a leadership role is literally just an addition of meanings to the word lead. In an interview, you want to make sure that the ways you can provide value to the company don't get buried under everything else that might come up. In a leadership role, it's important to keep those value creation methods at the forefront, but also to remember to actually lead. You no longer have to worry about creating all of that value on your own, instead you can help enable those under you to create additional value more expeditiously as a team. IDK, I've only had one managerial role, over 2 other people, so these are more thoughts than true experience.
Note that I described that as an addition of meanings, not a replacement. There's a major difference in a manager that has stopped caring and forces their employees to carry all the weight, and one that still cares and is able to help balance value creation between themselves and their team.
I'd say that in regard to leading, “lead with value” makes me think of having our own values and believing in them and kind of praising them in a sense, so that the people that follow us can know what to expect if they follow us.