Start experimenting by putting the 2 things in place you say you are missing:
1. create a validated learning model
2. Stop focusing on vanity metrics; replace with user growth, cohort analysis or growth metrics.

Do not just read Lean principles; APPLY them.

Also,
What are you doing to brand your company?
What are you doing to engaging people who have the problem your service solves?
Does it actually solve their problem? Do you know what their problems are? What do THEY think their problems are?

Its great to see that you are looking to adopt lean development methodologies to iterate and grow your business.

I have seen larger organizations that were actually stuck in their efforts to maintain/grow their business without experimenting on new concepts/opportunities. The result was a smaller nimbler startup that had been experimenting was able to disrupt & take market share.

Here are a few things you could try to introduce a culture of experimentation & constant learning of the market you operate in.

- Researching the market your online service operates in will yield ideas on potential trends, customer needs, pain points to solve etc that you can experiment on.

- Have a small team with flexibility to experiment via creation of prototypes /MVPs. These don't need a lot of full-out functionality. Think lean as in just a few web pages/ flows to address the identified needs

- Validate with a sample of current users or new set of users through a reachout, try A/B testing different concepts so you narrow down to the most valuable set of features/capabilities

You will learn a lot, and that is the best part where in if some of your concepts fail, atleast you learn about it sooner than later.

Happy to share more feedback over a call. There are several tools/methodologies that really support lean development. Feel free to reach out.

Good luck!

I've had to do something like this for an established company I work for to grow subscribers, as well as a startup I'm a part of.

It will be hard to give you any specific advice without knowing your exact business model and services.

But I would start with your own data and your current customers. Why did they buy from you? How did they hear about you? What do they like about the product and what can you improve?

Analyze your sales funnel and website metrics. Do you have a lot of leads but low conversion or vice versa? Once you answer that drill down to get a solution.

Where are your leads or highest converting customers coming from? Can you double down or exploit anything there?

Then start a list of areas to test with specific hypothesis and a process to test, analyze and iterate.

Great question.
To start out I'll say be careful with trying to implement the new thing you have read about. Just because you just came across this approach doesn't necessarily make them good for your business.
Lean startup methodology calls for new business minimal viable product launch. You didn't say why type of business you are in so this might be the right perspective for you.
What you mentioned tho is Growth Hacking. You are in a phase of business where can no longer grow it, I actually focus on serving this demographic. Part of how I deliver my services is through growth hacking.
Your web developers need to be savvy enough to implement marketing tactics 101 online as well as understand your business to make the appropriate changes, create landing conversion pages, a/b test different demographics, add or remove features, properly leverage the right social media with potential actual interested individuals.

look through my previous answers to find out more ways to grow a business. Or give me a call as this is a loaded question, and you didn't give much specific.