Please describe what you mean by a Review Mode. If you mean the Zoom box that comes up, No LR doesn't have that but you can zoom "in" in many different ratios.
In the Library module, you can use the Loupe mode to view, rate, pick/reject. I believe there is even an auto-advance feature that can be turned on.
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The Lightroom panels can be hidden by [Shift+TAB]
Press 'E' for LoupE (single image) view.
L&R Cursor keys scroll forward backward. (But without the fancy scroll of images in view like Bridge Review mode - who needs 'fancy'?)
If you are flagging picks 'P' or deletes 'X', then having the [Caps Lock] key on will automatically advance the image when you P or X.
Another 'trick' is (with caps lock on) place the left hand fingers on the four keys [ ~ 1 2 3 ], the right hand on the cursor keys.
The '~' tilde key (under the little finger) will flag as Pick, the 123 keys will star rate 1,2,3 stars. And the caps-lock auto-advances. To advance without a Pick flag or Star- press a L/R cursor key with the right hand.
Press 'G' for the Grid view and [Shift+TAB] to return to normal panel views
The Bridge Review mode allows you to 'fix' one image to the side with the up/down cursor keys, then move other images into view with left/right cursor keys.
This effect to compare two images that are 'apart' in the library is known as Survey Mode in Lightroom (Press 'N' ) then with the mouse select images to compare from the filmstrip below. Select any two to view them side-by-side, or select several to see them together on the screen.
I'm a loyal Adobe customer for 12 years, subscribe to the full CC plan, but what you want for this job is Photo Mechanic.