I am not in a league currently. But I always bowl right after leagues let out. I do wonder what it would be like to bowl with a fresh coat of oil on the lanes.

Is there a big difference in lane conditions during league vs. after league when the lanes have been bowled on quite a bit?

No matter where i go I bowl right after leagues let out late at night usually. Some places boards 1-10 are way too dry and it forces me to move left(boards 11-15 usually).

Sometimes I wouldn't mind playing boards 1-10, will I need a light oil ball in order to do this if i find that this area is very, very dry?

When we start out in league we always have fresh lanes. They are old wood and it gets hot in our alley as we have no air con. Oil goes quite quickly too and makes a bit of an erratic shot.
Now if we play a back match after league the lanes are dry preety much all over but especially in the track area.
Ive found the best way to stay competitive is to change my release to a more up the back rather than around the ball. You do leave the odd 10 pin because of a weak shot that looked good but its better than having balls that look good acting erratically.
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Happy go lucky bowler from the UK.
   Did someone say tough luck