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there are two sorts of lintel in common use
hollow pressed steel - this you attack with an ordinary HSS drill with no hammer action HSS drills are black or blue.
Reinforced concrete - this you attack with a TCT masonry bit (if you look at the tip, you will see it has a squarish pice of alloy notched and brazed into the tip and use hammer action on your drill Masonry drills are silvery coloured. The tips might be painted.
A budget cordless drill may have insufficient power, but you can buy a corded drill (with switchable hammer action) that will do the job.
Very occasionally you will be going into reinforced concrete and hit the reinforcing steel. In this case it is best to move up or down an inch and try again. more often you will be going into RC and hit a very hard, flinty stone. The masonry bit will go through this, with the hammer.
A masonry bit will not cut through steel
An HSS bit will not cut through concrete. Hammer action will ruin it almost immediately.
Your hole needs to go into the brick, block or lintel at least an inch after you have gone through the plaster. So assume you have to drill a 2-inch (50mm) deep hole. If the hole is too wide and the plasplug is loose, start a new thread in DIY called "Plasplug is loose in hole in wall" and I will tell you the magic trick.