Convert variable framerate ~60 FPS to constant 60 FPS losslessly
To start with: your version of Handbrake is old. Version 1.0.3 came out very recently, it's got some improvements over that older version.

Second, CQ0 is not actually "lossless." It's aiming for "lossless" quality, but it's going to bump up against the data rate limitations of the H.264 Level, so while it might need, say, 100MbPS at a given point to achieve "lossless" compression, Level 4.0 might be capping it at 20MbPS or something like that. Note in the Encoding Settings readout on your export file it lists "vbv_maxrate=20000," that's where your bitrate is capped. So to get as close to lossless as possible you'd need something like Level 5.2.

So ratcheting up your H.264 level will improve quality, but Premiere may end up chugging very hard on it. H.264 is really bad for editing. It's very computationally complex, largely because it doesn't store each frame separately (called Intraframe compression) but it takes batches of frames (called a Group of Pictures, or GOP) and compresses them together, in such a way that any one frame within a GOP will depend on the surrounding frames in order to reproduce a complete image. This is called Interframe compression, and the number of frames in a GOP depends on the parameters set at encode time, and may even be variable (not typical), but you can see what those parameters in MediaInfo by noting the line that says "Format settings, GOP" ("N=30" means 30 frames per GOP), or looking at the encoding settings where it notes "keyint" (Keyframe Interval). So needing to decode all 30 frames to show you any one frame is very CPU and RAM intensive.

If you've got the storage I'd recommend considering using DNxHD, which is a "mezzanine" (editing friendly) codec that preserves quality, considered "virtually lossless," but has low CPU/RAM impact. The catch is very high bitrates. So we're talking ~130-200GB/hr at 1080p59.94. The other catch is that DNxHD has very limited supported resolutions and frame rates. There's also CineForm which is just as high a quality, but far more flexible, and both CineForm and DNxHD are natively supported by Premiere (CineForm in 2015 and later) but last I checked CineForm support in other tools, like ffmpeg, is lacking.

So are more editing-friendly solution would be to use ffmpeg to make DNxHD with a command line the following:

ffmpeg -i (input file).mp4 -c:v dnxhd -b:v 290M -c:a pcm_s16le -r 60 (output).mxf


That would make DNxHD with uncompressed audio in an MXF Op1a file. You could also whack .mov on the end there and make a Quicktime file instead just as easily. Note that -r sets the output frame rate. You could try using H.264 in ffmpeg by changing the video codec (-c:v), but you'll run into the same limitations as you would working with Handbrake, so I don't know if it's really worth it to go into that here.