I've come in at Limehouse with a 70ft narrowboat with a JP2 engine on several occasions, and tried 3 different methods The direct approach, cutting straight across, with the boat at 45 degrees to the tide,slipping sideways with the tide, is great until you get just to the entrance. As your bows get into the slack water the current swings your stern downstream, and you have to be quick at manoeuvering.With a shorter boat, and more instant horsepower, you could be OK, but I've smacked into the upstream corner of the entrance more than once.The second way, going just past the entrance and coming up against the ebb tide, worked OK but be prepared to be pushed against the downstream wall, and "scrape" around the corner into the lock.
The third, and possibly least traumatic, way I've tried is to get across to the north side of the river a quarter of a mile or so before the lock. Once there, go as slowly as possible, (forwards) ensuring you still have steerage way.Keep as close to the shore as you can, so that you are out of the current as much as possible, but make sure you don't run aground! You can get surprisingly close to the shore without touching. As you turn into the lock cut, any following current will help your stern around. It worked for me!