We have Custom object 'XXX' as a related list in Lead, during conversion of Lead to Account,the related lists of lead is not being carried to the account and also the related list records of lead is being deleted.Why does it happen?Is there any option that the related lists of lead will be carried to accounts?Can we map it like we do it for custom fields?Need suggestions. Please advice?
For custom related lists you have to write your own logic to transfer the related records. Either through Trigger or Process Builder.
Here are some links may be helpful to you.