Btw, when I compared the LCD2 and HD600 it was in terms of tonality/frequency response neutrality only - not bass impact, detail, or anything else.
If you end up getting one of the Stax tube amps (one of the SRM-T1 variants or the SRM-006), they pair very well with the Lambdas. I would recommend the SR-Lambda (~$275), the SR-Lambda Signature (~$475), and the SR-Lambda Nova Signature (~$475). All are very good headphones and will showcase the Stax sound. You could use one of them until the SR-009 arrives and it pairs pretty well with those tube amps as well. The SR-007 however doesn't pair very well with the Stax tube amps, so that would change your upgrade path if you decide to go down that road.