How does luck continue to be a factor in the plot? Use text evidence.

Bilbo is lucky enough to navigate all of the barrels with his companions to shore and safety.

So you see Bilbo had come in the end by the only road that was any good. It might have been some comfort to Mr. Baggins shivering on the barrels, if he had known that news of this had reached Gandalf far away and given him great anxiety, and that he was in fact finishing his other business (which does not come into this tale) and getting ready to come in search of Thorin's company.

They would have been surprised, if they could have seen what happened down by the shore, after they had gone and the shades of night had fallen. First of all a barrel was cut loose by Bilbo and pushed to the shore and opened. Groans came from inside, and out crept a most unhappy dwarf. Wet straw was in his draggled beard; he was so sore and stiff, so bruised and buffeted he could hardly stand or stumble through the shallow water to lie groaning on the shore. He had a famished and a savage look like a dog that has been chained and forgotten in a kennel for a week. It was Thorin, but you could only have told it by his golden chain, and by the colour of his now dirty and tattered sky-blue hood with its tarnished silver tassel. It was some time before he would be even polite to the hobbit.