Sharpen An Image ?

First of all do any conversions you need but forget PNG or JPG as these are designed to create and image for use on the web where the resolution of screen and thus the picture is quite low (72DPI for Apple and 96DPI for Windows ), I would suggest that you only make one conversion step to Uncompressed TIFF format or at least keep conversions to an absolute minimum as each conversion degrades the image .

The basic Lightroom tools for image manipulation are also available in Adobe Bridge (as part of the Camera Raw package) - Unlike lightroom and Photoshop, Bridge is available free of charge Its True: Adobe Bridge CC Is Completely Free for Everyone, for Life! | ProDesignTools

I sharpen images by use of a combination of the Sharpening and Noise Reduction tools

Always work on a 100% view of the image as any other will not show the real state of the pixels

With adobe tools the both mentioned have a range of 0 - 100, (I assume %), what I have found is the best image result is achieved by making the total of the two tools equal 100, ie use the sharpen tool and set to eg 55, then use the Noise reduction and set this to 45 - play about with these values to give the best image you can - Both of the tools have other controls which control the area of influence of the tool and these can be adjusted to suit.

Always remember to regularly switch image size to your required output size to show the actual progress.

Free graphics packages such as GIMP - GNU Image Manipulation Program may also have reasonable tools for this task, and there is also, the now free, (thanks Google), Google Nik Collection but this needs a container application to use their Sharpener Pro, (time to check out the 30 Day Free trial of Lightroom or Photoshop Maybe ? )

I have just checked and Have found that the Google Nik Collection is compatible with Bridge, in addition to Photoshop and Lightroom, So if you install bridge and then install the NIK tools you will have free access to the NIK tools including Sharpener pro and dFine, (Noise Reduction).

Drawing 433971 | National Trust Collections seems to be the image you are interested in, which they make available on that page as a "low res image".

"SummaryAn ink and wash plan headed, 'Belton House Ground Plan', Showing out buildings with drains, culverts, fire mains, river and spring water services, cess pools, emptying valves and stop cocks etc. Linen backed paper and signed R. Basford, Clerk of Works, Brownlow Estate, Belton. 2nd October 1935.
View more details"

Like many National Trust Images, and other assets in their collections, they offer the image for sale to raise funds for maintenance of properties, land and their contents, with an "Order this image" link on the page link above.

That may be the only way you can obtain a legible legitimate copy.