Leave the egg out on the counter for an hour or let it sit in a bowl of warm water for 5 minutes.
Place 1/4 cup of the olive oil , the egg, mustard powder, and salt in a blender, food processor, mixing bowl, or glass jar. Mix thoroughly with an emulsion blender.
While the blender is running, slowly drizzle in the remaining 1 cup olive oil.
After you've added all the oil and the mixture has emulsified, add the lemon juice, blending on low or stirring to incorporate.