LCY is very easy, all SIDs stop at 3000 ft, no stepped climb
Not strictly true
only the BPK stops at 3000
DVR/LYD/SAM stops at 4000
CPT stops at 5000
CLN stops at 6000
Most aircraft are given a climb restriction of 3000ft only - as the stepped climb has been busted in the past with LHR descending to 4000ft on top. Also, there may be traffic inbound via LAM on a shortcur dropping to 4000ft
Apart from that, everything else you say is bang on and what we would expect.