The Bible does not lie, but liars lie. Since Noah had been commanded to build the ark -- a huge ship -- long before the Flood (120 years before), how could he have been "in great trouble"? As for Lot, God already knew that Lot and his family were to be delivered from wrath, therefore He specifically sent two angels to Sodom. So it was Sodom that was "in great trouble", not Lot.
Being in the midst of such a sinful situation is the great trouble Noah and Lot lived in. The Great Tribulation is described as how life was at the time of Noah before the flood:
Mat 24:37 But as the days of Noe were, so shall also the coming of the Son of man be.
Mat 24:38
For as in the days that were before the flood they were eating and drinking, marrying and giving in marriage, until the day that Noe entered into the ark,
Mat 24:39 And knew not until the flood came, and took them all away; so shall also the coming of the Son of man be.
So if we compare the times of and second coming, before the flood would be equal to the time of the Great Tribulation, and the flood is the coming of Jesus. The idea of fleeing from the coming wrath is the rapture. For Noah it was by boat, for Lot it was by foot with angels. Both situations are after a period of wickedness and sin, then rapture or taken away safely to a safe place for a new life, then the coming of Jesus and wrath. One by water, one by fire in the two examples. The end times wrath will be via the sword of the Lord and the vials of wrath.
Luk 17:26 And as it was in the days of Noe, so shall it be also in the days of the Son of man.
Luk 17:27 They did eat, they drank, they married wives, they were given in marriage, until the day that Noe entered into the ark, and the flood came, and destroyed them all.
Luk 17:28 Likewise also as it was in the days of Lot; they did eat, they drank, they bought, they sold, they planted, they builded;
Luk 17:29 But the same day that Lot went out of Sodom it rained fire and brimstone from heaven, and destroyed them all.
Luk 17:30 Even thus shall it be in the day when the Son of man is revealed.
Notice order of events in both:
First: the wicked carried on like everything was normal - "They ate, drank, and married each other" "they ate, drank, bought and sold, planted and builded"
second: they good people taken into or away to safety - "Noe entered into the ark" "Lot went out of Sodom"
third: The wrath of God - "and the flood came" "fire and brimstone fell from heaven"
fourth: The wicked are killed - "the flood destroyed them all" "fire and brimstone destroyed them all"
Same thing will happen at the end of the Tribulation.
Everything will seem normal to people. Then the rapture will occur taking the good people away. Then the wrath of God will come and the wicked will be slain. Same order of events, same results. The only difference in the methods of saving the good and killing the wicked. The past events happen more than once in order to teach us what to expect in the future.