Preheat a grill pan over high heat.
Brush the romaine spears with some lemon oil and season with salt and pepper, to taste. Put the spears on the grill pan and cook, turning once, until grill marks appear and the lettuce begins to wilt, about 2 minutes total. Immediately remove from the grill to a serving platter and sprinkle each half with about 2 tablespoons of the crumbled blue cheese.
With a sharp knife, cut the peel and pith from the orange. Carefully remove the orange segments by cutting them lengthwise away from the membrane, into a bowl. Squeeze the juice from the membrane over the segments and slowly whisk in 2 tablespoons lemon oil until combined. Season with salt and pepper, to taste, then add the shallots and stir to combine.
Drizzle the citrus vinaigrette and orange sections over the grilled romaine spears and garnish with the remaining blue cheese.