A Bossing stick is what you need, use a fibre glass one to avoid marking the lead.
Start from the top and gently work down the lead to form it in tight.
If you want to be accurate, finish with a chase wedge.
You need a bossing stick and a dresser. You can buy these items fairly cheaply from Toolstation. There is no need to heat the lead up. Just hold the edge of the lead steady with your left hand and start with the bossing stick dressing the lead in with your right hand. Finish off with the dresser. It doesn't have to be really tightly dressed in, that will result in the lead becoming too thin or splitting.
Also don't clip the lead too tightly either or the clips will spring open when the lead expands. You need a 6mm (or more) expansion space from where the clip bends over to the edge of the lead.
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