1986 LeBaron convertible, 2.2L T2 with A413. 1989 J convertible dash and console modified to fit.
I had this issue with a couple of later lock units I got out of a junk yard. The ignition lock is an eight cut system, odd number slides on one side even on the other, the slides when lined up properly allow the locking bar to retract. I believe it was on here I posted pictures of the assembly and how it comes apart. If it is only one key that does that, a new key may fix the problem. If not Dorman sells two different ignition locks, one is just a basic lock cylinder with 2 keys and full instructions on rekeying it to your keys, the other is a more complex (and expensive) automatic rekeying cylinder.