The second is Lynchburg

Not as font.
However, this free form lettering uses fishtail or moustache terminals in the style of several Tuscan fonts.
The first is Hessian.

logo for the restuarant
https://www.barbershop-paris.com/
Identity created by
http://www.tyrsa.fr/barbershop-paris/
Tyrsa probably modified a plain font to create the spurred, embossed and shadowed style for the letters.

Monotype Grotesque Std Extra Condensed would seem to work as a base for this customization.

The "gothic" in your specimen is usually known as a grotesque or grotesk, a 19th century style of sans serif.
You can get an almost exact match by using Founders Grotesk Bold. Compare your specimen to the character set produced by Identifont:

Follow the link for details on individual letters.

It would be helpful if you could give some information on the source of this old specimen.

The citation [Baltimore Type Foundry (1832)] in your other old font request* is very helpful in searching for a substitute.

* https://www.dafont.com/forum/read/347686/baltimore-type-foundry-1832

Perhaps dervived from Cortez, a phototype dating from 1977.

Edited

Created by the Walden Font Company and sold as part of their The Wild West Press font set.

A modern calligrapher has produced a poster in a similar style to the titling for Deus salve o Rei, which is available for for purchase as a print:
https://hyvyys.deviantart.com/art/Bastard-Secretary-494785926

The _D_ and _R_ are also calligraphy with a broad nib and are similar to style of of the Gothic Bastarda.
Calligrapher Gothic Bastard is an approximate match but the top rhs of _R_ is a broken stroke rather than a smooth loop.
Note that this suggestion was first made by Heron2001 https://www.dafont.com/forum/read/342573/deus-salve-o-rei

Looks like calligraphy with a broad nib using lower case letters in the general style of Rotunda, Rundgotish or Italian Gothic. Some of the letters in Rotunda Pommerania, such as _e_ and _o_ are an approximate match while others are different.

Some incising effects added by user.

Width expanded by user.

Repeating letters are different and I doubt that this is a font.
For a font with somewhat similar style you could try Kitchen Bold.

Stencil D by URW. The number sign in other versions of Stencil doers not match #SARANNOSOLANI

With apostrophe from somewhere else

Keep on Truckin' FW -- NOT THE FONT USED TO MAKE THE LETTERS -- cound be distorted to approximate RUBBER SOUL

Handlettered in a psychedelic style.
Doobie -- NOT THE FONT USED TO MAKE THE LETTERS -- cound be distorted to approximate RUBBER SOUL

My reading of the article linked in my post is that, although the new facebook logo has significant differences from Klavika, it is indeed derived from Klavika.