Goofs

In Thom's discussion with Cobcroft it's implied that U-boats travel underwater and surface in order to attack. It's actually the opposite. WWII era subs ran mostly on diesel, which needed to be vented to the outside, and stayed on the surface most of the time. They only submerged when they were about to attack, running on comparatively limited battery power.

A key plot point is the German sinking of an American ocean liner by German u-boats. In reality, the German Navy did not target passenger ships from neutral nations during the Battle of the Atlantic. Instead they targeted military vessels and civilian cargo ships.

The Nazi deception prior to the landing at Dover did nothing to reduce the power of the Royal Navy, it merely concentrated it in the wrong place. The RN would have simply responded to the Dover landings by steaming back into the Channel and destroying the German boats. This would have resulted in a sort of "reverse Dunkirk" where a significant portion of the German Army would have been trapped in Britain, cut off from supplies and at the mercy of the British.

The German invasion of Britain does not make any sense. In real life, the Nazis called off Operation Sealion, their planned invasion of Britain, because they lacked either air or naval superiority over Britain, both of which were seen as prerequisites for an invasion. In the world of Lola, Britain has even greater air and naval superiority over Germany, and yet the invasion goes forward.

The Nazis are seen as making extensive use of air-power during their invasion of Britain. However, it was previously established that the Luftwaffe was heavily decimated by Lola's predictions during the Battle of Britain, to the point where they have to call off operations. If they didn't have enough air-power to continue bombing Britain then they didn't have enough to provide air cover for an invasion.