A lightsaber can cut through anything and deflect laser blasts easily, right? So could a ship be built with its hull lined up with thousands to lightsabers? I mean, when turned on, it could easily deflect lasers and destroy other ships just by going through them. Is something like this possible?
There are several possible problems with this suggestion. Most significant among these though would be the access to lightsaber, or "Kyber," crystals. The following is taken from an article on Wookieepedia.
Kyber crystals were rare, Force-attuned crystals that grew in nature and were found on scattered planets across the galaxy.1 They were used by the Jedi1 and the Sith2 in the construction of their lightsabers. As part of Jedi training, younglings were sent to the Crystal Caves of the ice planet of Ilum to harvest crystals and then construct their own lightsabers.
We can see that these crystals were already very rare and that "harvesting" them required the involvement of Jedi. This makes finding and successfully mining them highly improbable. Thus, any commercial venture would be both highly risky and expensive.
Now, imagine the size of of a common starfighter and the number of lightsabers required to fully cover that ship, both it terms of height and width. Let's assume, as you suggest, that 1,000 lightsabers could fully cover a ship.
According to Wookieepedia, one lightsaber costs between 20,000 to 500,000 credits. Multiplying that by 1,000 gives a total cost between 20,000,000 and 500,000,000 credits just for additional shielding. This is nearly 3,333.3 times the cost of an X-Wing in the Legends continuity.
Note, I am using Legends information for the cost of an X-Wing for the sake of the argument. I will update this answer should the cost of an X-Wing be given in the Canon universe.
Thus, due to both the limited access to Kyber crystals as well as the high cost of lightsabers, such a ship design would be highly impractical and unfeasible.