The first round for local candidates is an in-person at their offices downtown, lasts about an hour, and is divided into two parts: a Q&A and 1-2 cases. Lake makes it very clear that they're looking for people with an established consulting skill set, and their interview process reflects this. They asked uncomplicated questions, asking me to walk through my resume and about prosaic details like what I'm reading right now.
The case component is pretty straightforward and will include a business problem Lake has recently or is actively tackling. If you're unfamiliar with the case interview format, pick up Cosentino's Case in Point and practice like it's your job. The interviewer was fair but firm in responding to me throughout the case, offering both affirming and detracting comments throughout. Be aware that, at this juncture, the case is very brief (more back of the envelope than true case), so get your questions done quickly and have an answer ready within 15 minutes. I took 25, and it was clear by the end of it that I had taken too long - had I locked down the scope of the question earlier, I should have been able to finish in 10.
Seattle candidates: don't go in to this interview expecting Accenture/Deloitte/Hitachi. Lake is trying to position themselves on level with McKinsey/Bain/BCG, and this comes through in both their recruiting & interview strategies. They're a boutique firm (~13 employees including the partners), but heavily recruit nationwide. They interview many, many candidates but accept almost none of them. Among the half dozen people I know who interviewed with them, not a single one got a second round. Their prospect mining list includes all of the Ivys, Princeton, Stanford, etc. My interviewer (who was an Analyst) had a master's in electrical engineering, was in his late 20s, and probably wary of being BSd at by some upstart undergrad.
Anecdotal: in keeping with their preference for candidates with consulting skills, Lake seems to put strong emphasis on client interaction soft skills, so be extremely diligent about communicating promptly and clearly, responding to all e-mails, confirming important information, getting contact information whenever you don't have it, and following up proactively.