Lewis Method

The Lewis method is a 4x4 speedsolving method that utililzes Direct Solving and Roux Methodbased steps to create a method that is both efficient(movecount comparable to Hoya or Meyer) and 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 Cube 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
 solve a 1x3x4 block around the right center
 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. 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.
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 a few ways to solve L5E, and the suggested way has changed more than once. Currently The fastest and most lookaheadefficient way is 4look L5E, in which you use both DF pieces as "buffers" and then directly solve 2 pieces at a time, which takes 4 looks on average. Often you will get only 2 edges messed up at the end of L5E. in this case, you can use one of ~12 L2E cases(of which half are mirrors, so about 6 algs)(You May need to conjugate the algorithm). Here is a tutorial for 4 look L5E
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 slightly higher than Yau method