Do you know what the yarn is (ie is there a label left?). Failing that, if you know what weight it is (DK, Aran etc) you can get ideas from Ravelry. Click on the 'yarn' tab if you know what it is, then enter the name and it will come up with a description, and a number of projects made from it. If you click on that, you will find suitable patterns and see what they look like knitted up in your yarn.
If you don't know the exact yarn, click on the 'patterns' tab and then 'advanced search' and use the filters to enter the weight and anything else you want to include or exclude. Again, it will come up with lots of suggestions.
Lavender needn't be 'old lady'. You can jazz it up with nice jewellery or scarves. Or what about making a knitting bag, or bedsocks and matching HWB cover?