When you join BA you are a 'First Officer' with two stripes.
After four years you are promoted to 'Senior First Officer' and get three stripes.
That's it until you make Captain with four stripes.
There is no difference between SH and LH. Plenty of LH two-stripers and plenty of SH three-stripers.
You could go straight from two to four stripes if you bid successfully for an unpopular command during your first four years.
There is also a 'seven year interview' where they need to see that you've actually got an unfrozen ATPL so that you can go to pay point eight. Until you achieve it, you're stuck on pay point seven. This only applies (obviously) to Senior First Officers.
There used to be some sort of 'cap' on LH SFOs' pay (16 years?) if they hadn't bid for a SH command by that point but that may have gone now.
The whole structure is rooted in history and assumes a bright-eyed 20-year-old joining straight out of Hamble. It's a bit archaic when you're dealing with DEPs who may have been training captains in a previous life. (Who, moi?)
BTW, the BMI merger (take-over?) saw many of their FOs keep their three stripes. Good for them!