The administration of the decedent's estate in a probate proceeding would not be a lawsuit. However, probate cases can also involve lawsuits and they are called ancillary actions. Examples would be a Will Contest lawsuit or a suit by a devisee against the executor or administrator claiming fraud or conversion. There are other types of lawsuits that can end up in probate court even though they may have been filed in county court at law or district court.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.
I just don't have enough context to answer your question. Sometimes, the existence of the probate "case" (really wouldn't call it a lawsuit) provides the basis to seek relief, like a writ of attachment. However, I need to know much more. Regardless, you don't walk into court and get a writ of attachment; it is an area where, unquestionably, you need an attorney's assistance.
There is no legal relationship created or implied by the exchange of message on this website. All statements are not to be construed as legal advice but as general guidance. In all cases, an attorney should be retained to review the full circumstances and deliver advice consistent with the information learned.