Steam the lobster until done, 5 to 10 minutes.
(If using frozen lobster, just steam until heated through.) Keep the lobster warm.
In a small saucepan over medium heat, melt the butter.
Add the flour and whisk until smooth.
Remove from heat and add the milk, cheese, lemon juice, and basil, whisking to combine.
Return to the heat and cook, stirring, until thick, 2 to 3 minutes.
In a medium-size bowl, toss the warm lobster with 1/2 cup of sauce, making sure to coat all the pieces.
Lay out the crepes and place 1/4 cup of the lobster mixture at the outer edge of each.
Roll each crepe and arrange seam side down in pairs on serving plates.
Drizzle with remaining sauce, sprinkle with paprika, if desired.