For those who love hand made lace.
Your hankie 1152-1153 is definitely Bedfordshire bobbin lace. Probably last half of the 19th c into about 1920. In the marked up photo below the red line mark out the path of the "trail", a design element which occurs in almost all Bedfordshire laces. Cluny also often has trails. But Bedfordshire trails have an organic quality. The green rings contain half stitch spots with raised tallies on top. This is also common to both Beds and Cluny. The blue rings show cloth "spiders" which often occur in Beds, also. The orange lines mark out some tallies.
The differences between Cluny and Bedfordshire, to a visual inspection, are largely a matter of style, which is very hard to describe. Below the photo there are links to 2 of my pinterest boards, for Bedforshire and Cluny laces. Studying those photos may help you to discover the stylistic differences.
Your lace 1154 is a "mixed tape lace". What looks slightly like a Bedfordshire trail is actually a machine woven straight tape/braid. The green rings show places where the tape was folded at the sharp points of the leaves. Tape lace can be entirely bobbin made, but when it is, there are no folds or gathers where the tape changes direction. The folds are what identifies this as a machine tape lace. But it does have hand made elements. The blue lines surround areas which contain needle lace fillings for the spaces between the tapes. There are several varieties of mixed tape lace. I'm not as knowledgable about those as I am about bobbin laces, so I can't give you a definite answer. This type of lace was very popular around 1900 among hobbyist lace makers. Many booklets of patterns and instructions were published c 1890-1910. An American version, called Battenberg, was very simple. This one is somewhat better than that (leaving aside the damage done by time and use). There is an English version called Branscombe point, which used many delicate needle lace fillings, and was very elaborate. This piece does not quite rise to that level. Date, most likely early 20th c.
My Mixed tape lace pinboard. Some of the pieces on it use a flat machine woven tape, some use a thicker crocheted tape. Both of those use needle lace fillings.
Lorelie, Thank you soooo much! I have purchased several books on different lace identification but its a bit overwhelming unless you actually see an item that you can inspect. Now that I have these for reference it will make it so much easier. Also, your pinterest boards are fantastic as they are broken down in various types. I will definitely be looking at them and trying to learn more. I am from the US but now live in the UK where there is more antique lace available.