1982 Copper LD Lincoln Cent, DDO / DDR.should I Grade?

I am not seeing a DDO or a DDR, can you provide a closeup of where exactly you see doubling? I just cannot see it.

I'll leave the Grading question for the experts, but as for your question about having this coin Graded by a service... unless this coin has sentimental value, having it "Graded" would be a losing proposition. This cent as is has a worth of about 3 cents (copper value wholesale), MS Graded '82 cents can be had for under $15, and with grading fees of about $50, well, as you can see, you'd be losing money. Sorry to be the bearer of bad news, just being honest. Your cent is a large date copper, the super rare one to look for is the small date '82-D copper. There are only a few known to exist. Sorry I couldn't be of more help.

From a grading perspective, I'm concerned about the series of scrapes above LIBERTY and the one gouge by Abe's bow tie. Otherwise, it is quite pleasing to me.

I'll say MS-62RD, pretty much a spender to me.