Migrate LightGBM integration

[y0z]

Motivation

Progress #4484.

Description of the changes

• Remove LightGBM integration and its tests.
• Please merge Add LGBM integration optuna-integration#81 before merging this PR.

[codecov]

Codecov Report

Attention: 15 lines in your changes are missing coverage. Please review.

Comparison is base (e905252) 89.83% compared to head (591a0ed) 89.31%.
Report is 5 commits behind head on master.

Files	Patch %	Lines
optuna/integration/lightgbm.py	0.00%	15 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #5249      +/-   ##
==========================================
- Coverage   89.83%   89.31%   -0.52%     
==========================================
  Files         213      206       -7     
  Lines       13707    13020     -687     
==========================================
- Hits        12313    11629     -684     
+ Misses       1394     1391       -3     

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[nabenabe0928]

Thank you for the PR, I found a critical problem we need to address, please take a close look!

[HideakiImamura]

@nabenabe0928 While you have already reviewed this PR, let me assign you as a reviewer.

[nabenabe0928]

Thanks for the modification!
I confirmed that the changes work perfectly!

$ pip install git+https://github.com/optuna/optuna-integration@main
$ pip install lightgbm
$ python -c "from optuna.integration.lightgbm import Dataset, train"

[HideakiImamura]

Thanks for the PR. I have several comments. PTAL.

[HideakiImamura]

LGTM.