'Rebecca' is a great violetta. I'd aim to grow it in light shade, or somewhere with less sun but still with a fairly open sky. As groundcover under rose beds would be a typical siting. You can grow it in more open sunny spots, but the cooler, damper places will make it less prone to red spider mite and powdery mildew. To get the plant well established can take more than a year, and until then do not let it dry out. After that, the plant should keep going for several years, providing you with plenty of material for division and months of flowers. Pick the flowers often - it is the best way of precluding seed pod formation. That way you get more flowers over a longer period, and you get to enjoy them indoors at close quarters, where the scent will be that much more noticeable.

So I would not plant it under you lilac. Apart from the shade, the soil can get very dry and depleted under lilacs, and the lilac roots can make it difficult to improve without causing the lilac to sucker.

Soil-wise, aim for a mix which retains a degree of moisture but still drains well, and which is in a spot which stays cool. (The foliage from a bed well-packed with flourishing violas will provide enough shade to keep the soil on the cool side.)

'Rebecca' or any other cultivar from the pansy side of the Viola genus, will not cross with violets. 'Rebecca' will produce seeds, and depending on what other pansy-relatives you have nearby, some of its progeny might resemble 'Rebecca' fairly well, but it will be very hit and miss (John Snocken may correct me on that). The best way to propagate it is by cuttings or division; there should be guidance elsewhere in this forum on pansy/viola cuttings - try the forum's Search facility.

You can use a root stimulator (bone meal would be an alternative) when planting out, but if it is a powder put it in with the soil rather than top-dressing - you don't want to encourage rooting towards the surface. If your root stimulator is applied as a liquid, it may be taken in by the foliage and/or it may get washed down to the roots as it rains; that's easier. Miracle Grow can work wonders at any time, especially on poorly pot-bound/starved plants. Vitax Q4 is the other good feed; as well as basic nutrients, it also contains trace elements.

For those wondering what 'Rebecca' looks like, have a look at http://myweb.tiscali.co.uk/heartsease/nvps/rebecca.htm

Jolly good luck; you stand a good chance of being delighted with 'Rebecca'.