L1B to H1B Transfer with 2 Months Gap

I have been selected this year with H1B lottery, I am currently working on L1B, and it is expiring in Mid July, is there a way not to exit the country from July to October. Please advice

Do you have anytime left from the 5 year max out of L1B? Also did the same employer raise your H1B as well?
If your L1B has not maxed out, you would be applying for extension and staying here until OCT under L1B with 180 day grace period and from OCT it would be H1B.
If it is maxed out(5years) in Mid July then it would mean moving out of the country right before max date and coming back with stamped H1B visa after OCT. From what I know you wouldn’t be able to stay during JUL-OCT if your L1B will max out in JUL and you do not have approved H1B yet and H1B will only be effective from OCT-2021.

Note: This is just based on my personal experience.