L1B to H1B transfer deadline

Urgently need an advice.

Situation: Currently on L1B maxing out in DEC 2021.
L1B expired in APRIL 2021 so filed extension and currently received no response on that from USCIS.
Same employer also filed H1B for COS this year and it’s picked in lottery.
Now employer is saying they cannot file petition for H1B as I already have an ongoing L1B extension petition with USCIS. I do not know if this is only my employer’s policy.
I am unsure if I have enough time to raise L1B to premium as it could get an RFE and responding to it would take time considering deadline for H1B filing is 30 June 2021.

Question: Is it legally okay with USCIS if same employer files two application (one L1B extension and another H1B for COS) ?
Or should there be only one application at a time with USCIS?

Appreciate your help and comments! Thanks!