Try bleeding the right front, you may have air in the system. While you are there have a look at the brake hose, with the engine running so the booster is working, get someone to tread on the pedal and see if the hose is perished and 'ballooning'. Have a good look at the caliper and make sure the seals are not leaking. You will already have noticed if the bleed nipple was leaking. All you can do then is trace the brake lines back to the master cylinder and make sure they are not leaking or crimped somewhere.
If you have to change anything then do both side at the same time.
As a last resort, look at the left front wheel, check that the bottom balljoint is good, also the track rod end and the control arm, if there was excessive movement/play in these then the wheel would snatch when you braked and maybe lock-up.