I'm not sure how readily available Autoglym is in certain parts of the USA but I know a lot of American wearers use Goo-Gone which you can buy in any Home Depot
http://www.homedepot.com/s/solvent%2520cleaner?NCNI-5

But if you search 'cleaning lace' you'll get links to LOTS of threads with various suggestions.
The advantage I find with soaking, rather than other techniques like 'Mirror slide' is that there is no rubbing of the lace base and I get next to no shedding.