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Even if there were Kosher witnesses and the bridegroom intend to mekadesh the bride, if the Shtar Kidushin was written by a Nochri a like a civil marriage, it is an invalid as a Kiddushin, as the questioner stated we need Kesiva Lishma Even Haezer 32,1. AssumingThis is assuming the civil marriage document itself is worth less than a shave Pruta (for everyone else and cannot be substituted as a monetary kiddushin Shave kesef )*.
The Gemara Gittin 23a says a Nochri writes autonimously and will on purposely not have in mind to think about the wedded woman when writing her name so there is no Kesiva Lishma and the KiddushinGett/Kiddushin is invalid:

בעינן כתיבה לשמה והא ודאי עובד כוכבים אדעתיה דנפשיה קעביד


*Note if he says that the woman is Mekudeshet to him with the civil marriage she is Safeik Mekudeshet (questionably married) and requires a Gett (Halachik Divorce) as stated in Shulchan Aruch Even Haezer 32,2 because the paper might be worth a Pruta elsewhere in the world and might be valid as Kidushei Shave Kesef. So since we are not sure, she needs a new Kidushin to get married or if she changes her mind she needs a Divorce.

Even if there were Kosher witnesses if the Shtar Kidushin was written by a Nochri a civil marriage is invalid as a Kiddushin, as the questioner stated we need Kesiva Lishma Even Haezer 32,1. Assuming the civil marriage document itself is worth less than a shave Pruta (for everyone else and cannot be substituted as a monetary kiddushin Shave kesef ).
The Gemara Gittin 23a says a Nochri writes autonimously and will on purposely not have in mind to think about the wedded woman when writing her name so there is no Kesiva Lishma and the Kiddushin is invalid:

בעינן כתיבה לשמה והא ודאי עובד כוכבים אדעתיה דנפשיה קעביד

Even if there were Kosher witnesses and the bridegroom intend to mekadesh the bride, if the Shtar Kidushin was written by a Nochri a like a civil marriage, it is an invalid Kiddushin, as the questioner stated we need Kesiva Lishma Even Haezer 32,1. This is assuming the civil marriage document itself is worth less than a shave Pruta (for everyone else and cannot be substituted as a monetary kiddushin Shave kesef )*.
The Gemara Gittin 23a says a Nochri writes autonimously and will on purposely not have in mind to think about the wedded woman when writing her name so there is no Kesiva Lishma and the Gett/Kiddushin is invalid:

בעינן כתיבה לשמה והא ודאי עובד כוכבים אדעתיה דנפשיה קעביד


*Note if he says that the woman is Mekudeshet to him with the civil marriage she is Safeik Mekudeshet (questionably married) and requires a Gett (Halachik Divorce) as stated in Shulchan Aruch Even Haezer 32,2 because the paper might be worth a Pruta elsewhere in the world and might be valid as Kidushei Shave Kesef. So since we are not sure, she needs a new Kidushin to get married or if she changes her mind she needs a Divorce.

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Even if there were Kosher witnesses if the Shtar Kidushin was written by a Nochri a civil marriage is invalid as a Kiddushin, as the questioner stated we need Kesiva LishmaKesiva Lishma Even Haezer 32,1. Assuming the Shtarcivil marriage document itself is worth less than a shave Prutashave Pruta (for everyone else and cannot be substituted as a monetary kiddushin as Shave PrutaShave kesef ) The.
The Gemara Gittin 23a says a Nochri writes autonimously and will on purposely not have in mind to think about the wedded woman when writing her name so there is no Kesiva Lishma and the Kiddushin is invalid:

בעינן כתיבה לשמה והא ודאי עובד כוכבים אדעתיה דנפשיה קעביד

Even if there were Kosher witnesses if the Shtar Kidushin was written by a Nochri a civil marriage is invalid as a Kiddushin, as the questioner stated we need Kesiva Lishma Even Haezer 32,1. Assuming the Shtar itself is worth less than a shave Pruta (for everyone else and cannot be a kiddushin as Shave Pruta) The Gemara Gittin 23a says a Nochri writes autonimously and will on purposely not have in mind to think about the woman when writing her name so there is no Kesiva Lishma:

בעינן כתיבה לשמה והא ודאי עובד כוכבים אדעתיה דנפשיה קעביד

Even if there were Kosher witnesses if the Shtar Kidushin was written by a Nochri a civil marriage is invalid as a Kiddushin, as the questioner stated we need Kesiva Lishma Even Haezer 32,1. Assuming the civil marriage document itself is worth less than a shave Pruta (for everyone else and cannot be substituted as a monetary kiddushin Shave kesef ).
The Gemara Gittin 23a says a Nochri writes autonimously and will on purposely not have in mind to think about the wedded woman when writing her name so there is no Kesiva Lishma and the Kiddushin is invalid:

בעינן כתיבה לשמה והא ודאי עובד כוכבים אדעתיה דנפשיה קעביד

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Even if there were Kosher witnesses if the Shtar Kidushin was written by a Nochri a civil marriage is invalid as a Kiddushin, as the questioner stated we need Kesiva Lishma Even Haezer 32,1. Assuming the Shtar itself is worth less than a shave Pruta (for everyone else and cannot be a kiddushin as Shave Pruta) The Gemara Gittin 23a says a Nochri writes autonimously and will on purposely not have in mind to think about the woman when writing her name so there is no Kesiva Lishma:

בעינן כתיבה לשמה והא ודאי עובד כוכבים אדעתיה דנפשיה קעביד