I have lilies in a border but want to know what to plant behind them.

If it's a sunny border, then how about Heleniums? They would be tall enough and carry on flowering when the lilies' petals drop. If you like 'hot' colours, then Crocosmia 'Lucifer' and other tall ones would tie in, too. Other tall perennials for a 'hot' theme - Heliopsis, Helianthus, Inula and Macleaya cordata. Cool it down with some Leucanthemum in white or cream.

I forgot to add Hollyhocks! They'd be a lovely background.