I have tried several procedures, as I too hate to loose all the neat colors some lumen prints have. I have found several things that seem to work well, and different papers and exposures need different processing. Unfortunately, a lumen print is a one of a kind, and you may improve it or ruin it. So here some things to try -
1. The type of paper makes a big difference. I find old papers which seem to give better results. Agfa papers from the 60's and 70's are especially nice. Old Kodak Polycontrast is good, as is old Unicolor (B&W) papers. Of more recent papers, I've had good results with Adorama VC RC papers.
2. Leave the print out in the light much longer than you think necessary. When the fixer fades/lightens it, it will still be richer.
3. After exposure, treat the paper with very dilute developer. I dilute Dektol 6:1 or 8:1, and treat the paper for a minute or less.
4. Try Chromoskadasic processing before fixing. This can really make some things bright. You may want to try this with just a little developer treatment as in item 3.
5. Sepia toning, either before or after fixing, or both gives interesting results.
6. I've had some good results with Rockland Colloid Polytoner used carefully.
The biggest factor seems to be the paper though. There's something about the old paper that new papers don't provide. I don't know if it's the amount of silver, different chemistry, age, or a combination of all three. We have an old photo store that had a lot of really old unsold paper of various brands which I bought for $1 a box. It had never been in a cooler, just sitting on a shelf. If you try to make a conventional print with any of it, it is fog city! For lumen prints, it's great.
Hope this helps a bit.