Lewis Method

The Lewis Method is a 4x4 speedsolving method that utilizes Direct Solving and Roux Methodbased steps to create a method that is pretty lookahead friendly. Some critics say it is a variant of the Stadler Method, even though Lewis is an improvement over both Stadler and Kenneth's Big Cubes Method, and only resembles Stadler in the first few steps.
Steps
Lewis Method is broken up into 5 steps:
 Solve 2 opposite centers(L and R centers)
 Solve a 1x3x4 block around the left center(Similar to Roux first block on 4x4)
 Solve a 1x3x4 block around the right center(Similar to Roux second block)
 CMLL(John Lewis also will try to solve some of step 5a before he executes CMLL)
 Step 5, aka Last 28 pieces. Broken up into 3 steps:
 Step 5a: solve the BD Block. This solves the B and D centers and the BD edge.
 There are Several ways to do this. the original way is to solve the D center(which sometimes done before CMLL), then the B center, then use the 2 free faces to solve the BD edge and insert it.
 Step 5B: solve Last 2 centers. This step is entirely made of the moves <l,r,U> and is simple to look ahead to while finishing the BD block.
 Step 5C: solve the Last 5 edges with commutators(10 wing pieces). This step is usually abbreviated to L5E.
 Step 5a: solve the BD Block. This solves the B and D centers and the BD edge.
Background
As the story goes, the Lewis Method was invented in early January 2017 by John Lewis(who goes by the username Shiv3r) while playing around with Kenneth's Big Cubes Method one evening. He decided the first step in KBCM, columns, is not efficient or fast. By doing 2 opposite centers, then First block and Second block like in Stadler. He then experimented with solving centers, then solving the D layer with commutators, then ELL afterwards. Because it was a long night and he was bored, he decided to do a few timed solves. To his surprise, within the first 5 or so solves he missed his PB by 2 seconds(He was using the Meyer method at the time and averaged sub2). After realizing his method had some potential, John experimented more, optimizing step 5 for both lookahead and efficiency and at the same time. In the process of developing the method, he created a new substep, L5E.
About a month later, Austin Moore revealed in a livestream on twitch that he had played around with the Lewis method. He then proceeded to get several fast solves with it. He has not switched from K4, but he is a very fast Lewis solver still.
Solving L5E
There are 3 current ways to solve L5E, each one made for a different skill level, and a different way to solve L2E.
 The first and simplest method is beginner's or 1atatime L5E, in which you use the 2 buffers in DF to directly solve one wing at a time.This method is suitable for beginners since it introduces some basic ideas about commutators without any real This is equivalent to 1atatime edge pairing in redux methods however, and is more of a stepping stone to faster and advanced L5E methods. Usually this method is associated with 1alg L2E, a 1algorithm method(3 if you include pure OLL & PLL parity) for solving L2E
 the Second Method is intuitive or 2atatime L5E. This is a method more suited for intermediate solvers. It directly solves 2 wings at a time with the intuitive 3cycle commutators. You use one of the 2 pieces at DF as the start to the cycle, then solve the piece that was in the spot the first wing went. There are some cases where you cannot do an intuitive commutator for the cycle you get, so you have to resort back to beginner's L5E for those cases. At this point you should start to learn the L2E algorithms(only 6 excluding mirrors).
 The fastest and most advanced method is called 4look L5E. 4look L5E is an expanded version of intuitive L5E. The differences are that 4look L5E adds on algorithms for the unintuitive cycles, some tricks for alreadypaired edges, and strategies to always avoid finishing the solve with pure OLL parity.
Pros
 solves pieces directly.
 movecount is comparable to Meyer method, Hoya method, and Straight Redux
 L5E is very fluid and lookahead friendly.
Cons
 No 3x3 stage
 Commutators are hard to understand at first
 average movecount is higher than Yau method
External links
 L2E algorithms(only learn group 2 and 3, grp. 1 should never pop up if you correctly do L5E.)
 Lewis Method Video Tutorial
 intuitive L5E tutorial
 John's Youtube channel, which has solves and tutorials for the Method