Apart from potentially more leaks, old lead pipe is often squashed, which reduces the flow of water through it. Probably it will be half-inch internal bore, might even be 3/8"
If you run a new plastic pipe, it can be substantially greater bore (typically 25mm though 32mm costs little extra and is the same amount of work) which will greatly improve the flow. I guarantee you will be amazed and delighted.
It does not need to follow the same route as the old one. It must be deep enough to pass the water co inspection. Run it all the way from the meter or stopcock under the pavement to the internal stopcock (or beyond) and take a 22mm copper internal pipe for the hot water, and another for the cold, before reducing the pipe size. Have a full bore stopcock (don't allow the plumbers to use a smaller one, which will constrict the flow but will be cheaper for them). Find out the cost of digging a trench before you decide on moling. Plumbers are weedy fellows with delicate little hands but builders can use a spade.
This will enable you to get stupendous showers and bath-filling if you get an unvented cylinder, and, if you have a combi boiler, will be less prone to sudden changes in pressure and temperature when other taps or appliances go on and off.
Replacing the lead may also reduce lead content in the drinking water, especially if you are in a soft water area.
Look up your local water co's policy on lead replacement. There might be a subsidy or they might dig up the pavement free or at a reduced rate. You will need a sample of drinking water tested BEFORE YOU START WORK so request this at once as they may be slow to make an appointment. As you may know, lead is damaging to the brain and nervous system, especially in babies and children.
Changing the pipe does not alter pressure, so will not stress your taps or appliances. Pressure is not the same as flow.