Fellow Midwest team here - We ran 4 Lemons races over the last 2 years and then ran our first Champcar race at Road America in October. I built the car knowing we might run both series. Here's what I did and we've never had a tech issue in either series.
Cage built to Lemons standards, which are a tad stricter than champ. Bought a kit from roll cage components and had it installed by a pro.
Champ requires a kill switch in the center dash or console, so we mounted ours there and connected a cable that runs over to the passenger window area so it can be pulled by a corner worker without them having to reach into the car.
To get ready for the Champ race we had to add a window net and a fire suppression system (now also required in Lemons ) - make sure your fire suppression system meets the minimum for whichever series is more strict (I think its Lemons). We also had to remove some theme-related spray-foam insulation to comply with Champ's "no 3D decorations" rule. Last but not least, to avoid massive points penalties we had to swap out the crappy adjustable shocks that were on the car when we got it with what ended up being a far better set of non-adjustable shocks that met champ's "2X" rule.
If you're running the OEM fuel system note that Lemons requires it to be 100% stock - vents, filler, etc., whereas champ allows you some modification. If you're running a cell take a very close look at the two sets of rules (we run OEM tank so I don't have any experience there).
Seat back braces are another area where there may be some discrepancies (another item we don't have).
That's about all I can think of on the tech side.
As far as classing goes, my suggestion is to pay most attention to the items that cost points in champ while keeping the spirit of Lemons in mind. We had done some stuff that was totally fine in Lemons (custom brackets made from "free" scrap to hold the OEM fan in place after we removed the AC condenser) that were going to cost us points in champcar and had to be removed or redone. That said, if we'd shown up at our first Lemons race with our shiny new non-adjustable Bilsteins we might have been tagged with some laps. In reality, once the Lemons judges are familiar with your car the level of scrutiny goes down and all those poly bushings you get for zero points in champ aren't an issue in Lemons, either.
Electric Mayhem Racing